Merge pull request #1 from FOSSEE/master

update fork. DONE

17 files changed, 864 insertions, 0 deletions

diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt
new file mode 100644
index 0000000..cae98ce
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file.txt
@@ -0,0 +1,3 @@
+file 'text.mp4'
+file 'LinearTransformation.mp4'
+file 'NonLinearTransformation.mp4'
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py
new file mode 100644
index 0000000..677f890
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py
@@ -0,0 +1,45 @@
+from manimlib.imports import *
+
+class text(Scene):
+    def construct(self):
+        text1 = TextMobject("For a grid, undergoing a linear transformation, all it's straight lines")
+        text1.scale(0.9)
+        text2 = TextMobject("must either remain straight lines or sends to a point in the grid formed")
+        text2.scale(0.9)
+        text1.move_to(ORIGIN+UP)
+        text2.move_to(ORIGIN)
+        self.play(Write(text1))
+        self.play(Write(text2))
+        self.wait()
+        self.play(FadeOut(text1),FadeOut(text2))
+
+class LinearTransformation(LinearTransformationScene):
+    CONFIG = {
+    "basis_vector_stroke_width": 3,
+    "leave_ghost_vectors": True,
+    }
+
+    def construct(self):
+        self.setup()
+        matrix = [[0.866,-0.5],[0.5,0.866]]
+        self.apply_matrix(matrix)
+        text = TextMobject("This is a Linear","Trasformation")
+        text[0].move_to(DOWN+4*LEFT)
+        text[1].move_to(1.5*DOWN+4*LEFT)
+        text.add_background_rectangle()
+        self.play(Write(text))
+        self.wait()
+
+class NonLinearTransformation(Scene):
+    def construct(self):
+        grid = NumberPlane()
+        self.play(ShowCreation(grid),run_time =2)
+        NonLinearTrans = lambda coordinates : coordinates + np.array([np.sin(coordinates[1]),np.sin(coordinates[0]),0,])
+        grid.prepare_for_nonlinear_transform()
+        self.play(grid.apply_function,NonLinearTrans)
+        text = TextMobject("While, this is not a","Linear Trasformation")
+        text[0].move_to(DOWN+4*LEFT)
+        text[1].move_to(1.5*DOWN+4*LEFT)
+        text.add_background_rectangle()
+        self.play(Write(text))
+        self.wait()
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py
new file mode 100644
index 0000000..577032d
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py
@@ -0,0 +1,193 @@
+from manimlib.imports import *
+
+class Rotation(GraphScene):
+    CONFIG = {
+        "x_min" : -5,
+        "x_max" : 5,
+        "y_min" : -5,
+        "y_max" : 5,
+        "graph_origin" : ORIGIN+3.5*LEFT,
+        "x_axis_width" : 7,
+        "y_axis_height" : 7
+        #"x_labeled_nums" : list(range(-5,6)),
+        #"y_labeled_nums" : list(range(-5,6)),
+    }
+
+    def construct(self):
+        XTD = self.x_axis_width/(self.x_max-self.x_min)
+        YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+        introText = TextMobject("Understanding Linear Transformations")
+        self.play(Write(introText))
+        self.wait(1)
+        
+        introText1 = TextMobject("Visually ... ")
+        introText1.move_to(DOWN)
+        self.play(Write(introText1))
+        self.wait(1)
+        self.play(FadeOut(introText), FadeOut(introText1))
+
+        Text1 = TextMobject("Let $\overrightarrow{v}$ be $2\hat{i}+3\hat{j}$")
+        Text2 = TextMobject("$\overrightarrow{v} = 2\hat{i}+3\hat{j}$")
+
+        Text1.move_to(4*RIGHT+2*UP)
+        Text2.move_to(4*RIGHT+1*UP)
+        self.play(Write(Text1))
+        self.wait()
+        self.play(Transform(Text1,Text2))
+        
+        self.setup_axes(animate=True)
+        arrow_v = Arrow(stroke_width = 3, start = self.graph_origin + 0.15*LEFT + 0.25*DOWN, end = self.graph_origin+2*XTD*RIGHT+3*YTD*UP+ 0.15*RIGHT + 0.25*UP)
+        self.play(ShowCreation(arrow_v))
+ 
+        Text_i = TextMobject("$\hat{i}$")
+        Text_i.move_to(self.graph_origin+0.5*XTD*RIGHT+0.5*YTD*DOWN)
+        Text_i.scale(0.75)
+        Text_j = TextMobject("$\hat{j}$")
+        Text_j.move_to(self.graph_origin+0.5*XTD*LEFT+0.5*YTD*UP)
+        Text_j.scale(0.75)
+ 
+        arrow_i = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT, end = self.graph_origin+1*XTD*RIGHT+ 0.25*RIGHT)
+        arrow_j = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*DOWN, end = self.graph_origin+1*YTD*UP+0.25*UP)
+        self.play(ShowCreation(arrow_i), ShowCreation(arrow_j), Write(Text_i), Write(Text_j))
+
+        Text_2i = TextMobject("$2\hat{i}$")
+        Text_2i.move_to(self.graph_origin+1*XTD*RIGHT+1*YTD*DOWN)
+        Text_3j = TextMobject("$3\hat{j}$")
+        Text_3j.move_to(self.graph_origin+1*XTD*LEFT+1.5*YTD*UP)
+
+        arrow_2i = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT, end = self.graph_origin+2*XTD*RIGHT+ 0.25*RIGHT)
+        arrow_2i.set_color(YELLOW)
+        arrow_3j = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*DOWN, end = self.graph_origin+3*YTD*UP+0.25*UP)
+        arrow_3j.set_color(RED)
+        self.wait(0.5)
+        self.play(Transform(arrow_i,arrow_2i), Transform(arrow_j,arrow_3j), Transform(Text_i,Text_2i), Transform(Text_j,Text_3j))
+        self.play(ApplyMethod(arrow_j.move_to,self.graph_origin+2*XTD*RIGHT+1.5*YTD*UP) , ApplyMethod(Text_j.move_to,self.graph_origin+2.5*XTD*RIGHT+1.5*YTD*UP+ 0.15*RIGHT + 0.25*UP))
+
+        new_Text_v = TextMobject("$\overrightarrow{v}$")
+        new_Text_v.move_to(self.graph_origin+0.5*XTD*RIGHT+1.5*YTD*UP)
+        self.play(Write(new_Text_v))
+
+        new_arrow_i = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT, end = self.graph_origin+1*XTD*RIGHT+ 0.25*RIGHT)
+        new_arrow_i.set_color(YELLOW)
+        new_arrow_j = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*DOWN, end = self.graph_origin+1*YTD*UP+0.25*UP)
+        new_arrow_j.set_color(RED)
+
+        new_Text_i = TextMobject("$\hat{i}$")
+        new_Text_i.move_to(self.graph_origin+0.5*XTD*RIGHT+0.5*YTD*DOWN)
+        new_Text_i.scale(0.75)
+        new_Text_j = TextMobject("$\hat{j}$")
+        new_Text_j.move_to(self.graph_origin+0.5*XTD*LEFT+0.5*YTD*UP)
+        new_Text_j.scale(0.75)
+        
+        self.wait(1)
+
+        self.play(FadeOut(Text_i),
+        FadeOut(Text_j),
+        FadeOut(arrow_i),
+        FadeOut(arrow_j),
+        ShowCreation(new_arrow_i),
+        ShowCreation(new_arrow_j),
+        Write(new_Text_i),
+        Write(new_Text_j))
+
+        self.play(ApplyMethod(Text1.move_to,4*RIGHT))
+        Text3 = TextMobject("Let the be a linear transformation function")
+        Text3.scale(0.5)
+        Text4 = TextMobject("$T$ which rotates the vectors by angle of $90^{\circ}$")
+        Text4.scale(0.5)
+        Text3.move_to(4*RIGHT+3*UP)
+        Text4.move_to(4*RIGHT+2.5*UP)
+        self.play(Write(Text3), Write(Text4))
+        self.wait(2)
+        
+        Text6 = TextMobject(r"$\begin{pmatrix} 1 \\ 0 \end{pmatrix}$")
+        Text6.scale(0.75)
+        Text6.set_color(YELLOW)
+        Text6.move_to(self.graph_origin+1*XTD*RIGHT+1*YTD*DOWN)
+        Text7 = TextMobject(r"$\begin{pmatrix} 0 \\ 1 \end{pmatrix}$")
+        Text7.scale(0.75)
+        Text7.set_color(RED)
+        Text7.move_to(self.graph_origin+1*XTD*LEFT+1*YTD*UP)
+
+        self.play(Transform(new_Text_i,Text6))
+        self.play(Transform(new_Text_j,Text7))
+
+        Text5 = TextMobject(r"$\overrightarrow{v} = 2 $", r"$\begin{pmatrix} 1 \\ 0 \end{pmatrix}$", r"+3", r"$\begin{pmatrix} 0 \\ 1 \end{pmatrix}$")
+        Text5[1].set_color(YELLOW)
+        Text5[3].set_color(RED)
+        Text5.move_to(4*RIGHT)
+        
+        self.play(Transform(Text1, Text5))
+        self.wait()
+
+        arrow_modified_i = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*UP, end = self.graph_origin-(1*YTD*UP+0.25*UP))
+        arrow_modified_i.set_color(YELLOW)
+        arrow_modified_j = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT, end = self.graph_origin+1*XTD*RIGHT+ 0.25*RIGHT)
+        arrow_modified_j.set_color(RED)
+        
+        yellow_i = TextMobject(r"$\begin{pmatrix} 0 \\ -1 \end{pmatrix}$")
+        yellow_i.set_color(YELLOW).scale(0.75)
+        yellow_i.move_to(self.graph_origin + 1*XTD*DOWN + 1*YTD*LEFT)
+
+        red_j = TextMobject(r"$\begin{pmatrix} 1 \\ 0 \end{pmatrix}$")
+        red_j.set_color(RED).scale(0.75)
+        red_j.move_to(self.graph_origin + 1*XTD*UP + 1*YTD*RIGHT)
+
+        Text8 = TextMobject(r"$\overrightarrow{v}_{transformed} = 2 $", r"$\begin{pmatrix} 0 \\ -1 \end{pmatrix}$", r"+3", r"$\begin{pmatrix} 1 \\ 0 \end{pmatrix}$")
+        Text8[1].set_color(YELLOW)
+        Text8[3].set_color(RED)
+        Text8.move_to(4*RIGHT+1.5*DOWN)
+        Text8.scale(0.75)
+
+        new_Text__v = TextMobject("$\overrightarrow{v}_{transformed}$")
+        new_Text__v.scale(0.75)
+        arrow_modified_v = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT + 0.15*UP, end = self.graph_origin+2*XTD*DOWN+3*YTD*RIGHT+ 0.15*DOWN + 0.25*RIGHT)
+        self.play(Transform(arrow_v, arrow_modified_v), 
+        Transform(new_arrow_i, arrow_modified_i), 
+        Transform(new_arrow_j, arrow_modified_j),
+        Transform(new_Text_i,yellow_i),
+        Transform(new_Text_j,red_j),
+        FadeOut(new_Text_v),
+        ApplyMethod(new_Text__v.move_to,self.graph_origin+3*XTD*RIGHT+0.5*YTD*DOWN),
+        Write(Text8))
+
+        self.play(FadeOut(Text1), FadeOut(Text3), FadeOut(Text4), ApplyMethod(Text8.move_to,4*RIGHT+3*UP))
+        
+        Text9 = TextMobject(r"$\overrightarrow{v}_{transformed} = 2 $", r"$\hat{i}_{transformed}$", r"+3", r"$\hat{j}_{transformed}$")
+        Text9[1].set_color(YELLOW)
+        Text9[3].set_color(RED)
+        Text9.move_to(4*RIGHT+2*UP)
+        Text9.scale(0.5)
+
+        self.play(Write(Text9))
+
+        v_transformed = TextMobject(r"$\overrightarrow{v}_{transformed} \equiv T(\overrightarrow{v})$")
+        v_transformed.scale(0.75).move_to(4*RIGHT+UP)
+        i_transformed = TextMobject(r"$\hat{i}_{transformed} \equiv T(\hat{i})$")
+        i_transformed.set_color(YELLOW).scale(0.75).move_to(4*RIGHT)
+        j_transformed = TextMobject(r"$\hat{v}_{transformed} \equiv T(\hat{j})$")
+        j_transformed.set_color(RED).scale(0.75).move_to(4*RIGHT+DOWN)
+
+        self.play(Write(v_transformed), Write(i_transformed), Write(j_transformed))
+        self.wait(3)
+
+        Text10 = TextMobject(r"$T(\overrightarrow{v}) = $", r"$\begin{pmatrix} 3 \\ -2 \end{pmatrix}$")
+        Text10[1].set_color(BLUE_E)
+        Text10.move_to(4*RIGHT+1*UP)
+        Text10.scale(0.75)
+
+        self.play(Write(Text10), ApplyMethod(v_transformed.move_to,4*RIGHT+2*UP), FadeOut(i_transformed), FadeOut(j_transformed), FadeOut(Text9))
+        self.wait(1)
+
+        self.play(FadeOut(self.axes), 
+        FadeOut(arrow_v), 
+        FadeOut(new_arrow_i), 
+        FadeOut(new_arrow_j), 
+        FadeOut(new_Text_i), 
+        FadeOut(new_Text_i), 
+        FadeOut(new_Text_j), 
+        FadeOut(new_Text__v), 
+        FadeOut(Text10), 
+        FadeOut(v_transformed),
+        FadeOut(Text8))
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py
new file mode 100644
index 0000000..a7856a5
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file3_Uniform_Scaling.py
@@ -0,0 +1,91 @@
+from manimlib.imports import *
+
+class Scaling(GraphScene):
+    CONFIG = {
+        "x_min" : -5,
+        "x_max" : 5,
+        "y_min" : -5,
+        "y_max" : 5,
+        "graph_origin" : ORIGIN+3.5*LEFT,
+        "x_axis_width" : 7,
+        "y_axis_height" : 7
+        #"x_labeled_nums" : list(range(-5,6)),
+        #"y_labeled_nums" : list(range(-5,6)),
+    }
+
+    def construct(self):
+        XTD = self.x_axis_width/(self.x_max-self.x_min)
+        YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+        introText = TextMobject("Scaling")
+        self.play(Write(introText))
+        self.wait(1)
+        self.play(FadeOut(introText))
+
+        introText = TextMobject("Uniform Scaling")
+        self.play(Write(introText))
+        self.wait(1)
+        self.play(FadeOut(introText))
+
+        Text1 = TextMobject("Let $\overrightarrow{v}$ be $3\hat{i}+3\hat{j}$")
+        Text2 = TextMobject("$\overrightarrow{v} = 3\hat{i}+3\hat{j}$")
+
+        Text1.move_to(4*RIGHT+2*UP)
+        Text2.move_to(4*RIGHT+1*UP)
+        self.play(Write(Text1))
+        self.wait()
+        self.play(Transform(Text1,Text2))
+        
+        self.setup_axes(animate=True)
+        arrow_v = Arrow(stroke_width = 4, start = self.graph_origin + 0.15*LEFT + 0.15*DOWN, end = self.graph_origin+3*XTD*RIGHT+3*YTD*UP+ 0.15*RIGHT + 0.15*UP)
+        vector_v = TextMobject(r"$\vec{v}$")
+        vector_v.move_to(self.graph_origin + 1*XTD*RIGHT + 2*YTD*UP )
+        self.play(ShowCreation(arrow_v),Write(vector_v))
+        scaling_factor = TextMobject(r"Scaling Factor = $\frac{4}{3}$")
+        scaling_factor.scale(0.75)
+        scaled_vector = TextMobject(r"$T(\vec{v}) = \frac{4}{3} \left[ \begin{array} {c} 3 \\ 3 \end{array} \right] = \left[ \begin{array} {c} 4 \\ 4 \end{array} \right]$")
+        scaled_vector.set_color(DARK_BLUE)
+        scaled_vector.scale(0.75)
+        scaling_factor.move_to(4*RIGHT)
+        scaled_vector.move_to(4*RIGHT+DOWN)
+        self.play(Write(scaling_factor))
+        self.wait()
+        self.play(Write(scaled_vector))
+
+        transformed_arrow_v = Arrow(stroke_width = 2, start = self.graph_origin + 0.15*LEFT + 0.15*DOWN, end = self.graph_origin+4*XTD*RIGHT+4*YTD*UP+ 0.15*RIGHT + 0.15*UP)
+        transformed_arrow_v.set_color(DARK_BLUE)
+        transformed_vector_v = TextMobject(r"$T(\vec{v})$")
+        transformed_vector_v.move_to(self.graph_origin + 4.5*XTD*RIGHT + 4.5*YTD*UP )
+        transformed_vector_v.set_color(DARK_BLUE)
+        self.play(ShowCreation(transformed_arrow_v), Write(transformed_vector_v))
+
+        self.wait()
+
+        represent_text1 = TextMobject("Representation of scaling")
+        represent_text2 = TextMobject("of vectors in point form")
+        represent_text1.move_to(4*RIGHT+3*UP)
+        represent_text2.move_to(4*RIGHT+2*UP)
+        self.play(Write(represent_text1), Write(represent_text2))
+
+        dot_init = Dot(self.graph_origin+3*XTD*RIGHT+3*YTD*UP)
+        dot_trans = Dot(self.graph_origin+4*XTD*RIGHT+4*YTD*UP)
+        
+        self.play(ApplyMethod(vector_v.move_to,self.graph_origin+2.5*XTD*RIGHT+2.5*YTD*UP),
+        ApplyMethod(transformed_vector_v.move_to,self.graph_origin+4.5*XTD*RIGHT+4.5*YTD*UP),
+        ShowCreation(dot_init), 
+        Transform(arrow_v,dot_init),
+        Transform(transformed_arrow_v,dot_trans))
+
+        self.wait(2)
+
+        self.play(FadeOut(dot_init), 
+        FadeOut(arrow_v), 
+        FadeOut(transformed_arrow_v), 
+        FadeOut(represent_text1), 
+        FadeOut(represent_text2),  
+        FadeOut(self.axes), 
+        FadeOut(scaling_factor),
+        FadeOut(scaled_vector),
+        FadeOut(transformed_vector_v),
+        FadeOut(vector_v),
+        FadeOut(Text1))
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py
new file mode 100644
index 0000000..91f098e
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear.py
@@ -0,0 +1,53 @@
+from manimlib.imports import *
+
+class Hori_Shear(GraphScene):
+    CONFIG = {
+        "x_min" : -5,
+        "x_max" : 5,
+        "y_min" : -5,
+        "y_max" : 5,
+        "graph_origin" : ORIGIN+3.5*LEFT,
+        "x_axis_width" : 7,
+        "y_axis_height" : 7
+        #"x_labeled_nums" : list(range(-5,6)),
+        #"y_labeled_nums" : list(range(-5,6)),
+    }
+
+    def construct(self):
+        XTD = self.x_axis_width/(self.x_max-self.x_min)
+        YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+        Text1 = TextMobject("Before"," Horizontal")
+        Text1[0].set_color(YELLOW)
+        Text2 = TextMobject("Shear Transformation")
+
+        Text1.move_to(4*RIGHT+2*UP)
+        Text2.move_to(4*RIGHT+1*UP)
+        
+        self.setup_axes(animate=False)
+        arrow_i = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT, end = self.graph_origin+1*XTD*RIGHT+ 0.25*RIGHT)
+        arrow_j = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*DOWN, end = self.graph_origin+1*XTD*UP+0.25*UP)
+        arrow_i.set_color(YELLOW)
+        arrow_j.set_color(YELLOW)
+
+        square = Polygon(self.graph_origin,self.graph_origin+2*XTD*RIGHT, self.graph_origin+2*XTD*RIGHT+2*YTD*UP,  self.graph_origin+2*YTD*UP)
+        square.set_color(DARK_BLUE)
+        self.play(ShowCreation(square), Write(Text1), Write(Text2), ShowCreation(arrow_i), ShowCreation(arrow_j))
+        self.wait(1)
+
+        Text3 = TextMobject("After"," Horizontal")
+        Text3[0].set_color(RED)
+        Text4 = TextMobject("Shear Transformation")
+
+        Text3.move_to(4*RIGHT+2*UP)
+        Text4.move_to(4*RIGHT+1*UP)
+        
+        trans_arrow_i = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT, end = self.graph_origin+1*XTD*RIGHT+ 0.25*RIGHT)
+        trans_arrow_j = Arrow(stroke_width = 3, start = self.graph_origin + 0.15*DOWN + 0.15*LEFT, end = self.graph_origin+1*XTD*UP+1*YTD*RIGHT+0.25*UP+0.25*RIGHT)
+        trans_arrow_i.set_color(RED)
+        trans_arrow_j.set_color(RED)
+        
+        rhombus = Polygon(self.graph_origin,self.graph_origin+2*XTD*RIGHT, self.graph_origin+4*XTD*RIGHT+2*YTD*UP,  self.graph_origin+2*XTD*RIGHT+2*YTD*UP)
+        square.set_color(DARK_BLUE)
+        self.play(Transform(arrow_i,trans_arrow_i), Transform(arrow_j,trans_arrow_j), Transform(square,rhombus), Transform(Text1,Text3), Transform(Text2,Text4))
+        self.wait(1)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif
new file mode 100644
index 0000000..9bef1b6
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file4_Horizontal_Shear_gif.gif
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py
new file mode 100644
index 0000000..718e4e0
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear.py
@@ -0,0 +1,52 @@
+from manimlib.imports import *
+
+class Ver_Shear(GraphScene):
+    CONFIG = {
+        "x_min" : -5,
+        "x_max" : 5,
+        "y_min" : -5,
+        "y_max" : 5,
+        "graph_origin" : ORIGIN+3.5*LEFT,
+        "x_axis_width" : 7,
+        "y_axis_height" : 7
+        #"x_labeled_nums" : list(range(-5,6)),
+        #"y_labeled_nums" : list(range(-5,6)),
+    }
+
+    def construct(self):
+        XTD = self.x_axis_width/(self.x_max-self.x_min)
+        YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+        Text1 = TextMobject("Before"," Vertical")
+        Text1[0].set_color(YELLOW)
+        Text2 = TextMobject("Shear Transformation")
+
+        Text1.move_to(4*RIGHT+2*UP)
+        Text2.move_to(4*RIGHT+1*UP)
+        
+        self.setup_axes(animate=False)
+        arrow_i = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*LEFT, end = self.graph_origin+1*XTD*RIGHT+ 0.25*RIGHT)
+        arrow_j = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*DOWN, end = self.graph_origin+1*XTD*UP+0.25*UP)
+        arrow_i.set_color(YELLOW)
+        arrow_j.set_color(YELLOW)
+
+        square = Polygon(self.graph_origin,self.graph_origin+2*XTD*RIGHT, self.graph_origin+2*XTD*RIGHT+2*YTD*UP,  self.graph_origin+2*YTD*UP)
+        square.set_color(DARK_BLUE)
+        self.play(ShowCreation(square), Write(Text1), Write(Text2), ShowCreation(arrow_i), ShowCreation(arrow_j))
+        self.wait(1)
+
+        Text3 = TextMobject("After"," Vertical")
+        Text3[0].set_color(RED)
+        Text4 = TextMobject("Shear Transformation")
+
+        Text3.move_to(4*RIGHT+2*UP)
+        Text4.move_to(4*RIGHT+1*UP)
+        
+        trans_arrow_i = Arrow(stroke_width = 3, start = self.graph_origin + 0.15*DOWN + 0.15*LEFT, end = self.graph_origin+1*XTD*UP+1*YTD*RIGHT+0.25*UP+0.25*RIGHT)
+        trans_arrow_j = Arrow(stroke_width = 3, start = self.graph_origin + 0.25*DOWN, end = self.graph_origin+1*XTD*UP+ 0.25*UP)
+        trans_arrow_i.set_color(RED)
+        trans_arrow_j.set_color(RED)
+        
+        rhombus = Polygon(self.graph_origin,self.graph_origin+2*XTD*UP, self.graph_origin+2*XTD*RIGHT+4*YTD*UP,  self.graph_origin+2*XTD*RIGHT+2*YTD*UP)
+        self.play(Transform(arrow_i,trans_arrow_i), Transform(arrow_j,trans_arrow_j), FadeOut(square), ShowCreation(rhombus), Transform(Text1,Text3), Transform(Text2,Text4))
+        self.wait(1)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif
new file mode 100644
index 0000000..7ca323f
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file5_Vertical_Shear_gif.gif
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py
new file mode 100755
index 0000000..01a0cef
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file6_linear_transformation.py
@@ -0,0 +1,27 @@
+from manimlib.imports import *

+class LinearTrans(LinearTransformationScene,MovingCameraScene):

+        CONFIG = {

+        "basis_vector_stroke_width": 1,

+        "leave_ghost_vectors": True,

+        }

+

+        def setup(self):

+            LinearTransformationScene.setup(self)

+            MovingCameraScene.setup(self)

+        

+        def construct(self):

+            self.setup()

+            self.camera_frame.save_state()

+            self.play(self.camera_frame.set_width, 7)

+            matrix = [[0.866,-0.5],[0.5,0.866]]

+            self.apply_matrix(matrix)

+            arc1 = Arc(radius = 0.25,angle=TAU/12)

+            arc2 = Arc(radius = 0.25,angle=TAU/12,start_angle=TAU/4)

+            text1 = TextMobject(r"$\theta$")

+            text1.scale(0.5)

+            text1.move_to(0.5*UP+0.125*LEFT)

+            text2 = TextMobject(r"$\theta$")

+            text2.scale(0.5)

+            text2.move_to(0.5*RIGHT+0.125*UP)

+            self.play(ShowCreation(arc1),ShowCreation(arc2),Write(text1),Write(text2),run_time=1)

+            self.wait()

diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
new file mode 100755
index 0000000..b400f93
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
@@ -0,0 +1,34 @@
+from manimlib.imports import *

+

+class Orthogonal(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes()

+        self.play(ShowCreation(axes))

+        self.move_camera(phi=30*DEGREES,theta=-45*DEGREES,run_time=3)

+        line1 = Line(start = ORIGIN,end = -3*LEFT)

+        line1.set_color(DARK_BLUE)

+        tip1 = Polygon(-LEFT,-0.8*LEFT-0.2*DOWN,-0.8*LEFT-0.2*UP)

+        tip1.move_to(-3*LEFT)

+        tip1.set_opacity(1)

+        tip1.set_fill(DARK_BLUE)

+        tip1.set_color(DARK_BLUE)

+

+        arrow2 = Line(start = ORIGIN,end = -3*UP)

+        arrow2.set_color(DARK_BLUE)

+        tip2 = Polygon(DOWN,0.8*DOWN-0.2*RIGHT,0.8*DOWN-0.2*LEFT)

+        tip2.move_to(3*DOWN)

+        tip2.set_opacity(1)

+        tip2.set_fill(DARK_BLUE)

+        tip2.set_color(DARK_BLUE)

+        arrow2.set_color(DARK_BLUE)

+

+        arrow3 = Line(start = ORIGIN,end = [0,0,3])

+        arrow3.set_color(DARK_BLUE)

+        tip3 = Polygon([0,0,3],[0,0,2.8]-0.2*RIGHT,[0,0,2.8]-0.2*LEFT)

+        tip3.set_opacity(1)

+        tip3.set_fill(DARK_BLUE)

+        tip3.set_color(DARK_BLUE)

+

+        self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3))

+        

+        self.wait()
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
new file mode 100644
index 0000000..0a28f22
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
@@ -0,0 +1,82 @@
+from manimlib.imports import *
+class OrthonormalBasis(GraphScene):
+    CONFIG = {
+        "x_min" : -6,
+        "x_max" : 6,
+        "y_min" : -4,
+        "y_max" : 4,
+        "graph_origin" : ORIGIN ,
+}
+
+    def construct(self):
+        self.setup_axes(animate=True)
+
+        XTD = self.x_axis_width/(self.x_max-self.x_min)
+        YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+        arrow1 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*RIGHT)
+        arrow1.scale(2.25)
+        arrow1.set_color(DARK_BLUE)
+
+        arrow2 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*LEFT)
+        arrow2.scale(2.25)
+        arrow2.set_color(DARK_BLUE)
+
+        square = Polygon(UP*0.4*YTD,0.2*(YTD*UP+XTD*RIGHT),ORIGIN,0.2*(YTD*UP+XTD*LEFT))
+        square.set_color(DARK_BLUE)
+        self.play(ShowCreation(arrow2), ShowCreation(arrow1), ShowCreation(square))
+
+        ortho = TextMobject("Orthonormal Vectors")
+        ortho.scale(0.75)
+        ortho.move_to(DOWN+3*RIGHT)
+        self.play(Write(ortho))
+        self.wait()
+        self.play(FadeOut(ortho))
+
+        arrow3 = Arrow(start = ORIGIN,end = YTD*3*UP+XTD*LEFT)
+        arrow3.scale(1.25)
+        arrow3.set_color(GOLD_E)
+        self.play(ShowCreation(arrow3))
+
+        arrow4 = Arrow(start = ORIGIN,end = YTD*UP+XTD*RIGHT)
+        arrow4.scale(1.8)
+        arrow4.set_color(GOLD_A)
+        
+        arrow5 = Arrow(start = ORIGIN,end = 2*YTD*UP-2*XTD*RIGHT)
+        arrow5.scale(1.3)
+        arrow5.set_color(GOLD_A)
+        
+        self.play(ShowCreation(arrow5), ShowCreation(arrow4))
+        
+        self.wait()
+
+        self.play(FadeOut(arrow1), FadeOut(arrow2), FadeOut(square))
+
+        self.wait()
+
+        text1 = TextMobject(r"$<v,v_1> v_1$")
+        text1.move_to(UP+2*RIGHT)
+        text1.scale(0.75)
+        text2 = TextMobject(r"$<v,v_2> v_2$")
+        text2.move_to(UP+3*LEFT)
+        text2.scale(0.75)
+        
+        text3 = TextMobject("v")
+        text3.move_to(YTD*3.5*UP+XTD*1.5*LEFT)
+
+        self.play(Write(text1), Write(text2), Write(text3))
+        self.wait()
+
+        line1 = DashedLine(start = YTD*UP+XTD*RIGHT, end = YTD*3*UP+XTD*1*LEFT)
+        line2 = DashedLine(start = YTD*2*UP+XTD*2*LEFT, end = YTD*3*UP+XTD*1*LEFT)
+        self.play(ShowCreation(line1),ShowCreation(line2))
+
+        self.wait()
+        
+        text = TextMobject(r"$v$ is the sum of projections","on the orthonormal vectors")
+        text[0].move_to(DOWN+3.2*RIGHT)
+        text[1].move_to(1.5*DOWN+3.2*RIGHT)
+        self.play(Write(text))
+        self.wait(2)
+        self.play(FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(text1), FadeOut(text2), FadeOut(text3), FadeOut(self.axes), FadeOut(line1), FadeOut(line2))
+        self.play(FadeOut(text))
diff --git a/FSF-2020/linear-algebra/linear-transformations/README.md b/FSF-2020/linear-algebra/linear-transformations/README.md
new file mode 100644
index 0000000..692201e
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/README.md
@@ -0,0 +1,9 @@
+# Contributer: Archit Sangal

+My Github Account : <a href="https://github.com/architsangal">architsangal</a>

+<br/></br>

+## Sub-Topics Covered:

++ Vector Space Homomorphisms (Linear Maps)

++ The Four Fundamental Subspaces

++ Rank-Nullity Theorem

++ Orthonormal basis

++ Gramm-Schmidt Orthogonalization Process

diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif
new file mode 100644
index 0000000..7d8d2e1
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py
new file mode 100644
index 0000000..afe4f9a
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.py
@@ -0,0 +1,30 @@
+from manimlib.imports import *
+
+class Column_Space(Scene):
+    def construct(self):
+
+        A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$")
+        A.move_to(2*UP)
+        A[1].set_color(color = DARK_BLUE)
+        A.scale(0.75)
+
+        self.play(Write(A),run_time = 1)      
+
+        CS_A = TextMobject(r"Column Space of $A = x_{1}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 2 \\ 3 \end{array} \right)$",r"$+x_{2}$",r"$ \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 2 \end{array} \right)$",r"$ + x_{3}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 4 \\ 3 \end{array} \right)$")
+        CS_A.move_to(1.5*LEFT+1*DOWN)
+        CS_A[1].set_color(color = DARK_BLUE)
+        CS_A[3].set_color(color = DARK_BLUE)
+        CS_A[5].set_color(color = DARK_BLUE)
+        CS_A.scale(0.75)
+
+        self.play(Write(CS_A),run_time = 2)
+
+        arrow1 = Arrow(start = 1.25*UP,end = 0.25*DOWN+1.75*LEFT)
+        arrow2 = Arrow(start = 1.35*UP+0.5*RIGHT,end = 0.25*DOWN+0.5*RIGHT)
+        arrow3 = Arrow(start = 1.25*UP+0.75*RIGHT,end = 0.25*DOWN+2.9*RIGHT)
+
+        Defn = TextMobject("Linear Combination of Columns of Matrix")
+        Defn.move_to(3*DOWN)
+
+        self.play(Write(Defn), ShowCreation(arrow1), ShowCreation(arrow2), ShowCreation(arrow3),run_time = 1)
+        self.wait(1)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py
new file mode 100644
index 0000000..b16a32a
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file2_Row_Space.py
@@ -0,0 +1,145 @@
+from manimlib.imports import *
+
+class Row_Space(Scene):
+    def construct(self):
+
+        Heading = TextMobject("Row Space")
+        defn1 = TextMobject("Definition 1: Row Space of a matrix is the linear combination of the rows of that matrix.")
+        defn2 = TextMobject("Definition 2: It is a vector space generated by a linear combination of the columns of $A^{T}$.")
+        equivalent = TextMobject(r"Definition 1 $\equiv$ Definition 2")
+
+        Heading.move_to(2*UP)
+        Heading.set_color(color = DARK_BLUE)
+
+        defn1.move_to(UP)
+        defn1.scale(0.75)
+
+        defn2.scale(0.75)
+
+        equivalent.move_to(DOWN)
+
+        self.play(Write(Heading))
+        self.play(Write(defn1))
+        self.play(Write(defn2))
+        self.play(Write(equivalent))
+
+        self.wait(2)
+        self.play(FadeOut(Heading),FadeOut(defn1),FadeOut(defn2),ApplyMethod(equivalent.move_to,2*UP))
+
+        how = TextMobject("Let us see, How?")
+        how.move_to(UP)
+        self.play(Write(how))
+        self.play(FadeOut(equivalent),FadeOut(how))
+
+        A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$")
+        A.move_to(2*UP+3*LEFT)
+        A[1].set_color(color = DARK_BLUE)
+        A.scale(0.80)
+
+        self.play(Write(A))
+
+        rows = TextMobject(r"Rows of A $\rightarrow$",
+        r"$\left( \begin{array}{c c c} 1 & 2 & 1 \end{array} \right)$,",
+        r"$ \left( \begin{array}{c c c} 1 & 3 & 1 \end{array} \right)$,",
+        r"$\left( \begin{array}{c c c} 2 & 1 & 4 \end{array} \right)$,",
+        r"$ \left( \begin{array}{c c c} 3 & 2 & 3 \end{array} \right)$")
+        rows.scale(0.75)
+        rows[1:5].set_color(DARK_BLUE)
+        self.play(Write(rows))
+
+        ac_defn1 = TextMobject("According to Definition 1 : ")
+        ac_defn1.move_to(DOWN)
+
+        RS_A = TextMobject(r"Row Space of $A = x_{1}$",
+        r"$\left( \begin{array}{c c c} 1 & 2 & 1 \end{array} \right)$",
+        r"$+x_{2}$",
+        r"$ \left( \begin{array}{c c c} 1 & 3 & 1 \end{array} \right)$",
+        r"$ + x_{3}$",
+        r"$\left( \begin{array}{c c c} 2 & 1 & 4 \end{array} \right)$",
+        r"$+x_{4}$",
+        r"$ \left( \begin{array}{c c c} 3 & 2 & 3 \end{array} \right)$")
+        RS_A.move_to(DOWN+DOWN)
+        RS_A[6].move_to(2*DOWN+DOWN)
+        RS_A[7].move_to(2*DOWN+2*RIGHT+DOWN)
+        RS_A[1].set_color(color = DARK_BLUE)
+        RS_A[3].set_color(color = DARK_BLUE)
+        RS_A[5].set_color(color = DARK_BLUE)
+        RS_A[7].set_color(color = DARK_BLUE)
+        RS_A.scale(0.75)
+
+        self.play(FadeOut(rows[0]),Transform(rows[1],RS_A[1]),Transform(rows[2],RS_A[3]),Transform(rows[3],RS_A[5]),Transform(rows[4],RS_A[7]))
+        self.play(FadeIn(ac_defn1), Write(RS_A))
+        self.wait(1)
+
+        self.play(FadeOut(rows[1]), FadeOut(rows[2]), FadeOut(rows[3]), FadeOut(rows[4]), FadeOut(RS_A), FadeOut(ac_defn1))
+
+        A_T = TextMobject(r"$A^{T} = $",r"$\left( \begin{array}{c c c c} 1 & 1 & 2 & 3 \\ 2 & 3 & 1 & 2 \\ 1 & 1 & 4 & 3 \end{array} \right)$")
+        A_T.move_to(2*UP+3*RIGHT)
+        A_T[1].set_color(color = DARK_BLUE)
+        A_T.scale(0.80)
+
+        self.play(Write(A_T))
+
+        change1 = TextMobject(r"Rows of $A\equiv$ Columns of $A^{T}$")
+        change2 = TextMobject(r"Columns of $A\equiv$ Rows of $A^{T}$")
+        change2.move_to(DOWN)
+
+        change3 = TextMobject(r"Row Space of $A$ = Linear Combination of",r"Rows","of",r"A")
+        change3.move_to(2*DOWN)
+        change3[1].set_color(DARK_BLUE)
+        change3[3].set_color(DARK_BLUE)
+
+        self.play(Write(change1))
+        self.play(Write(change2))
+        self.play(Write(change3))
+
+        columns = TextMobject("Columns")
+        columns.scale(0.6)
+        columns.set_color(DARK_BLUE)
+        columns.move_to(2*DOWN+4.1*RIGHT)
+
+        a = TextMobject(r"$A^{T}$")
+        a.set_color(DARK_BLUE)
+        a.move_to(1.95*DOWN+5.6*RIGHT)
+
+        self.wait(0.5)
+
+        self.play(Transform(change3[1],columns), Transform(change3[3],a))
+
+        equal = TextMobject(r"= Column Space($A^{T}$)")
+        equal.move_to(3*DOWN+0.5*RIGHT)
+
+        self.play(Write(equal))
+
+        self.play(FadeOut(A_T), FadeOut(change1), FadeOut(change2), FadeOut(change3), FadeOut(A), FadeOut(equal))
+
+        ac_defn1.move_to(3*UP)
+        RS_A.move_to(1.5*UP)
+        RS_A[6].move_to(UP)
+        RS_A[7].move_to(UP+1.5*RIGHT)
+        
+        self.play(Write(RS_A),FadeIn(ac_defn1))
+        
+        CS_AT = TextMobject(r"Row Space of $A = x_{1}$",
+        r"$\left( \begin{array}{c} 1 \\ 2 \\ 1 \end{array} \right)$",
+        r"$+x_{2}$",
+        r"$ \left( \begin{array}{c} 1 \\ 3 \\ 1 \end{array} \right)$",
+        r"$ + x_{3}$",
+        r"$\left( \begin{array}{c} 2 \\ 1 \\ 4 \end{array} \right)$",
+        r"$+x_{4}$",
+        r"$ \left( \begin{array}{c} 3 \\ 2 \\ 3 \end{array} \right)$")
+        CS_AT.move_to(1.5*DOWN)
+        CS_AT[1].set_color(color = DARK_BLUE)
+        CS_AT[3].set_color(color = DARK_BLUE)
+        CS_AT[5].set_color(color = DARK_BLUE)
+        CS_AT[7].set_color(color = DARK_BLUE)
+        CS_AT.scale(0.75)
+        
+        ac_defn2 = TextMobject("According to Definition 2 : ")
+        equivalent = TextMobject(r"Hence, Definition 1 $\equiv$ Definition 2")
+        equivalent.move_to(3*DOWN)
+
+        self.play(Write(CS_AT),FadeIn(ac_defn2))
+        self.play(Write(equivalent))
+
+        self.wait()
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
new file mode 100644
index 0000000..5c48a13
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
@@ -0,0 +1,3 @@
+file 'RN_Line.mp4'
+file 'RN_Point.mp4'
+file 'RN_SameDim.mp4'
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
new file mode 100755
index 0000000..e54276c
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
@@ -0,0 +1,97 @@
+from manimlib.imports import *

+class RN_Line(LinearTransformationScene):

+    def construct(self):

+

+        self.setup()

+        self.wait()

+        

+        predim = TextMobject("Dimension of this vector space is 2")

+        predim.move_to(DOWN+4*LEFT)

+        predim.scale(0.75)

+        predim.add_background_rectangle()

+        self.play(Write(predim))

+        self.wait()

+        self.play(FadeOut(predim))

+

+        afterlt = TextMobject("After Linear transformation")

+        afterlt.move_to(DOWN+4*LEFT)

+        afterlt.scale(0.75)

+        afterlt.add_background_rectangle()

+        

+        afterlt2 = TextMobject("Dimension of the vector space","changes to 1")

+        afterlt2[0].move_to(1.5*DOWN+4*LEFT)

+        afterlt2[1].move_to(2*DOWN+4*LEFT)

+        afterlt2.scale(0.75)

+        afterlt2.add_background_rectangle()

+        matrix = [[1,1],[1,1]]

+        self.apply_matrix(matrix)

+        self.play(Write(afterlt))

+        self.play(Write(afterlt2))

+        self.wait()

+        nullity = TextMobject("Hence, nullity = 1")

+        nullity.move_to(DOWN+4*LEFT)

+        self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))

+        self.wait(1)

+        self.play(FadeOut(nullity))

+

+class RN_Point(LinearTransformationScene):

+    def construct(self):

+        self.setup()

+        self.wait()

+        predim = TextMobject("Another One")

+        predim.move_to(DOWN+4*LEFT)

+        predim.scale(0.75)

+        predim.add_background_rectangle()

+        self.play(Write(predim))

+        self.wait()

+        self.play(FadeOut(predim))

+        afterlt = TextMobject("After Linear transformation")

+        afterlt.move_to(DOWN+4*LEFT)

+        afterlt.scale(0.75)

+        afterlt.add_background_rectangle()

+        afterlt2 = TextMobject("Dimension of the vector space","changes to 0")

+        afterlt2[0].move_to(1.5*DOWN+4*LEFT)

+        afterlt2[1].move_to(2*DOWN+4*LEFT)

+        afterlt2.scale(0.75)

+        afterlt2.add_background_rectangle()

+        matrix = [[0,0],[0,0]]

+        self.apply_matrix(matrix)

+        self.play(Write(afterlt))

+        self.play(Write(afterlt2))

+        self.wait()

+        nullity = TextMobject("Hence, nullity = 2")

+        nullity.move_to(DOWN+4*LEFT)

+        self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))

+        self.wait(1)

+        self.play(FadeOut(nullity))

+

+class RN_SameDim(LinearTransformationScene):

+    def construct(self):

+        self.setup()

+        self.wait()

+        predim = TextMobject("Let us look at another example")

+        predim.add_background_rectangle()

+        predim.move_to(DOWN+4*LEFT)

+        predim.scale(0.75)

+        self.play(Write(predim))

+        self.wait()

+        self.play(FadeOut(predim))

+        afterlt = TextMobject("After Linear transformation")

+        afterlt.move_to(DOWN+4*LEFT)

+        afterlt.scale(0.75)

+        afterlt.add_background_rectangle()

+        afterlt2 = TextMobject("Dimension of the vector space","remains to be 2")

+        afterlt2[0].move_to(1.5*DOWN+4*LEFT)

+        afterlt2[1].move_to(2*DOWN+4*LEFT)

+        afterlt2.scale(0.75)

+        afterlt2.add_background_rectangle()

+        matrix = [[1,1],[0,1]]

+        self.apply_matrix(matrix)

+        self.play(Write(afterlt))

+        self.play(Write(afterlt2))

+        self.wait()

+        nullity = TextMobject("Hence, nullity = 0")

+        nullity.move_to(DOWN+4*LEFT)

+        self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))

+        self.wait(1)

+        self.play(FadeOut(nullity))
\ No newline at end of file