Files added to Linear Transformations (Linear Maps)

7 files changed, 389 insertions, 0 deletions

diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/Animation.py b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/Animation.py
deleted file mode 100644
index e69de29..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/Animation.py
+++ /dev/null
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file1_Understand_Linear_Transformations_visually.py b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file1_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)/file1_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)/file2_Uniform_Scaling.py b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file2_Uniform_Scaling.py
new file mode 100644
index 0000000..a7856a5
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file2_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)/file3_Horizontal_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear.py
new file mode 100644
index 0000000..91f098e
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_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)/file3_Horizontal_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear_gif.gif
new file mode 100644
index 0000000..9bef1b6
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file3_Horizontal_Shear_gif.gif
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear.py b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear.py
new file mode 100644
index 0000000..718e4e0
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_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)/file4_Vertical_Shear_gif.gif b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear_gif.gif
new file mode 100644
index 0000000..7ca323f
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear Transformations (Linear Maps)/file4_Vertical_Shear_gif.gif