diff options
Diffstat (limited to 'FSF-2020/linear-algebra')
/file4_Horizontal_Shear_gif.gif?id=6718828cded8243922fd8820a36c5f2ed5e19fbc&id2=7741043e07cf71c0dc47a80d4cd71dbbcd2e09b8){kind=link}
/file5_Vertical_Shear_gif.gif?id=6718828cded8243922fd8820a36c5f2ed5e19fbc&id2=7741043e07cf71c0dc47a80d4cd71dbbcd2e09b8){kind=link}
29 files changed, 886 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)/file1_Understand_Linear_Transformations_visually.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_Understand_Linear_Transformations_visually.py index 577032d..577032d 100644 --- 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)/file2_Understand_Linear_Transformations_visually.py 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)/file3_Uniform_Scaling.py index a7856a5..a7856a5 100644 --- 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)/file3_Uniform_Scaling.py 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)/file4_Horizontal_Shear.py index 91f098e..91f098e 100644 --- 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)/file4_Horizontal_Shear.py 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)/file4_Horizontal_Shear_gif.gif Binary files differindex 9bef1b6..9bef1b6 100644 --- 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)/file4_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)/file5_Vertical_Shear.py index 718e4e0..718e4e0 100644 --- 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)/file5_Vertical_Shear.py 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)/file5_Vertical_Shear_gif.gif Binary files differindex 7ca323f..7ca323f 100644 --- 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)/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/The-Four-Fundamental-Subspaces/file1_Column_Space.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file1_Column_Space.gif Binary files differnew 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 diff --git a/FSF-2020/linear-algebra/vector-spaces/README.md b/FSF-2020/linear-algebra/vector-spaces/README.md index e69de29..03f6a03 100644 --- a/FSF-2020/linear-algebra/vector-spaces/README.md +++ b/FSF-2020/linear-algebra/vector-spaces/README.md @@ -0,0 +1,9 @@ +# Contributer: Simran Chhattani
+My Github Account : <a href="https://github.com/simranchhattani">simranchhattani</a>
+<br/></br>
+## Sub-Topics Covered:
++ Vector Spaces
++ Basis of a Vector Space and Subspace
++ Polynomial and Function Vector Space
++ Inner Product Spaces
++ Dual of a Vector Space
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Straight_Line_through_Origin.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Straight_Line_through_Origin.py new file mode 100644 index 0000000..5790d2e --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Straight_Line_through_Origin.py @@ -0,0 +1,48 @@ +from manimlib.imports import *
+from scipy import exp, sin, log,tan,cos
+class Straight_Line(GraphScene):
+ CONFIG = {
+ "x_min" : -4,
+ "x_max" : 4,
+ "y_min" : -4,
+ "y_max" : 4,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "x_labeled_nums" : list(np.arange(-4,5,1)),
+ "y_labeled_nums" : list(np.arange(-4,5,1)),
+ "graph_origin" : ORIGIN+0.7*DOWN,
+ "axes_color" : GREY,
+ "x_axis_width": 6,
+ "y_axis_height":6,
+ }
+ def construct(self):
+ self.setup_axes(animate=True)
+ line_1 = self.get_graph(lambda x : x, x_min=-3,x_max=3,color=YELLOW)
+ self.play(ShowCreation(line_1))
+ text1 = TextMobject("ax + by = 0",color=BLUE_B)
+ text1.shift(3*RIGHT+2*UP)
+ text1.scale(0.65)
+ dot = Dot(color=BLUE_B).shift(0.7*DOWN)
+ dot.scale(1.3)
+ self.play(ShowCreation(dot))
+ text2 = TextMobject("Line passing through the origin")
+ text2.scale(0.7)
+ text2.shift(3.5*UP)
+ self.play(ShowCreation(text1),ShowCreation(text2))
+ self.wait(1)
+ self.play(FadeOut(line_1),FadeOut(text2),FadeOut(text1))
+ text4=TextMobject("Line not passing through the origin")
+ text4.scale(0.7)
+ text4.shift(3.5*UP)
+ self.play(ShowCreation(text4))
+
+ line_2 = self.get_graph(lambda x : 2.5*x +1, x_min = -2, x_max=1, color = RED)
+ text3 = TextMobject(r"ax + by $\neq 0$",color=BLUE_B)
+ text3.scale(0.65)
+ self.play(ShowCreation(line_2))
+ text3.shift(1.5*RIGHT+2.2*UP)
+ self.play(ShowCreation(text3))
+ self.wait(1)
+
+
+
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py new file mode 100644 index 0000000..ada173e --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py @@ -0,0 +1,82 @@ +from manimlib.imports import *
+class Subspace_Example(Scene):
+ def construct(self):
+ sq = Square(side = 2, color=BLACK).shift(2*LEFT)
+ sq.set_fill(color=RED,opacity=350)
+ line1=Line(color=BLACK).shift(2*LEFT)
+ line1.rotate(np.pi/2)
+ line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)
+ line2.scale(0.5)
+ line3=Line(color=BLACK).shift(+1.5*LEFT)
+ line3.scale(0.5)
+ a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)
+ a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)
+ a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)
+ a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)
+ big_rect=Rectangle().scale(3).shift(0.5*DOWN)
+ big_rect.set_fill(color=GREY,opacity=350)
+ vec_space=TextMobject("$Vector Space$").scale(0.77).shift(4.5*RIGHT+3.5*UP)
+ sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.77).shift(3.8*RIGHT+2*UP)
+ self.play(ShowCreation(vec_space))
+ self.play(ShowCreation(big_rect),ShowCreation(sub))
+ self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))
+ rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)
+ rec.rotate(np.pi/2)
+ rec.set_fill(color=BLUE,opacity=350)
+ line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)
+ line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)
+ line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)
+ b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)
+ b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)
+ b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)
+ b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)
+ self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
+ self.wait(1)
+ text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)
+ text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)
+ self.play(ShowCreation(text1),ShowCreation(text2))
+ self.wait(3)
+ self.play(FadeOut(text1),FadeOut(text2))
+ rec.shift(3*LEFT+2.01*DOWN)
+ line4.shift(3*LEFT+2*DOWN)
+ line5.shift(3*LEFT+2*DOWN)
+ line6.shift(3*LEFT+2*DOWN)
+ b1.shift(3.1*LEFT+2.1*DOWN)
+ b2.shift(3.1*LEFT+2.1*DOWN)
+ b3.shift(2.9*LEFT+2*DOWN)
+ b4.shift(2.9*LEFT+2.3*DOWN)
+ self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
+ self.wait(2)
+
+ text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
+ text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
+ text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
+ self.play(ShowCreation(text3),ShowCreation(text4))
+ self.wait(3)
+ rec.set_fill(color=GREY,opacity=350)
+ self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))
+ sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)
+ sq1.set_fill(color=RED,opacity=350)
+ sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)
+ sq2.set_fill(color=RED,opacity=350)
+ rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)
+ rec1.set_fill(color=RED,opacity=350)
+ rec2=Rectangle(height=1.5,width=1,color=BLACK)
+ rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)
+ self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))
+ a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)
+ b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)
+ c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)
+ d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)
+ self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))
+ self.wait(2.3)
+ text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
+ text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)
+ text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)
+ self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))
+ self.wait(3)
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Unit_Circle.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Unit_Circle.py new file mode 100644 index 0000000..2973f08 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Unit_Circle.py @@ -0,0 +1,68 @@ +from manimlib.imports import *
+import numpy as np
+import math
+
+class Unit_Circle(GraphScene):
+ CONFIG = {
+ "x_min" : -3,
+ "x_max" : 3,
+ "y_min" : -3,
+ "y_max" : 3,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "x_labeled_nums" : list(np.arange(-3,4,1)),
+ "y_labeled_nums" : list(np.arange(-3,4,1)),
+ "graph_origin" : ORIGIN,
+ "axes_color" : GREY,
+ "x_axis_width": 6,
+ "y_axis_height":6,
+ }
+
+ def construct(self):
+ self.setup_axes(animate = True)
+ circle = Circle(radius=1,color=BLUE)
+ self.play(ShowCreation(circle))
+ dot1 = Dot(color=RED).scale(0.7)
+ dot1.shift(1*UP)
+ dot2 = Dot(color=RED).scale(0.7)
+ dot2.shift(1*LEFT)
+ dot3 = Dot(color=RED).scale(0.7)
+ dot3.shift(1*DOWN)
+ dot4 = Dot(color=RED).scale(0.7)
+ dot4.shift(1*RIGHT)
+ dot5= Dot(color=RED).scale(0.7)
+ dot6 = Dot(color=RED).scale(0.7)
+ dot5.shift(0.5*RIGHT+(math.sqrt(3)/2)*UP)
+ dot6.shift(0.5*LEFT+(math.sqrt(3)/2)*DOWN)
+ dot7 = Dot(color=RED).scale(0.7)
+ dot7.shift(math.sqrt(2)/2*RIGHT+math.sqrt(2)/2*UP)
+ dot8 = Dot(color=RED).scale(0.7)
+ dot8.shift(math.sqrt(2)/2*LEFT+math.sqrt(2)/2*UP)
+ dot9 = Dot(color=RED).scale(0.7)
+ dot9.shift(0.5*LEFT+(math.sqrt(3)/2)*UP)
+ dot10 = Dot(color=RED).scale(0.7)
+ dot10.shift(math.sqrt(3)/2*LEFT+0.5*UP)
+ dot11=Dot(color=RED).scale(0.7)
+ dot11.shift(math.sqrt(3)/2*RIGHT+0.5*UP)
+ dot12= Dot(color=RED).scale(0.7)
+ dot12.shift(math.sqrt(3)/2*LEFT+0.5*DOWN)
+ dot13=Dot(color=RED).scale(0.7)
+ dot13.shift(math.sqrt(2)/2*RIGHT+math.sqrt(2)/2*DOWN)
+ dot14=Dot(color=RED).scale(0.7)
+ dot14.shift(math.sqrt(2)/2*LEFT+math.sqrt(2)/2*DOWN)
+ dot15=Dot(color=RED).scale(0.7)
+ dot15.shift(math.sqrt(3)/2*RIGHT+0.5*DOWN)
+ dot16=Dot(color=RED).scale(0.7)
+ dot16.shift(0.5*RIGHT+(math.sqrt(3)/2)*DOWN)
+ self.play(ShowCreation(dot1),ShowCreation(dot2))
+ self.play(ShowCreation(dot3),ShowCreation(dot4))
+ self.play(ShowCreation(dot5),ShowCreation(dot6))
+ self.play(ShowCreation(dot7),ShowCreation(dot8))
+ self.play(ShowCreation(dot9),ShowCreation(dot10))
+ self.play(ShowCreation(dot11),ShowCreation(dot12))
+ self.play(ShowCreation(dot13),ShowCreation(dot14))
+ self.play(ShowCreation(dot15),ShowCreation(dot16))
+ self.wait(4)
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Straight_Line_Through_Origin.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Straight_Line_Through_Origin.gif Binary files differnew file mode 100644 index 0000000..b7695a4 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Straight_Line_Through_Origin.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif Binary files differnew file mode 100644 index 0000000..32b02be --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Unit_Circle.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Unit_Circle.gif Binary files differnew file mode 100644 index 0000000..165d040 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Unit_Circle.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/3D_Vector_Space.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/3D_Vector_Space.py new file mode 100644 index 0000000..70913eb --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/3D_Vector_Space.py @@ -0,0 +1,14 @@ +from manimlib.imports import *
+class ThreeDSpace(ThreeDScene):
+ def construct(self):
+ curve = ParametricFunction(
+ lambda x: np.array([
+ 0, -x , x]), color = YELLOW, t_min = -2, t_max = 2)
+ axes = ThreeDAxes()
+ axes.set_stroke(width=1,color=GOLD)
+ self.add(axes)
+ self.set_camera_orientation(phi = 70*DEGREES,theta =60*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.3)
+ self.play(ShowCreation(curve))
+ self.wait(6)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py new file mode 100644 index 0000000..70af123 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py @@ -0,0 +1,137 @@ +from manimlib.imports import *
+import numpy as np
+
+class vectorspace(GraphScene):
+ CONFIG={
+ "x_min": -7,
+ "x_max": 7,
+ "y_min": -7,
+ "y_max": 7,
+ "graph_origin": ORIGIN,
+ "x_axis_label":"$X$",
+ "y_axis_label":"$Y$",
+ "x_labeled_nums": list(np.arange(-7, 8,1)),
+ "y_labeled_nums": list(np.arange(-7, 8,1)),
+ "x_axis_width": 8,
+ "y_axis_height": 7,
+ "x_tick_frequency":1,
+ "axes_color": GREY,
+ "area_opacity": 3,
+ "num_rects": 10,
+ }
+ def construct(self):
+ XD = self.x_axis_width/(self.x_max- self.x_min)
+ YD = self.y_axis_height/(self.y_max- self.y_min)
+ a1=1*XD*RIGHT+2*YD*UP
+ a2=1*XD*RIGHT+1*YD*UP
+ vec1=Vector(direction=a1).set_color(RED_E)
+ vec1.shift(self.graph_origin)
+ vec2=Vector(direction=a2).set_color(YELLOW_E)
+ vec2.shift(self.graph_origin)
+ vec1_text=TextMobject(r"$\vec{a}$")
+ vec2_text=TextMobject(r"$\vec{b}$")
+ vec1_text=(vec1_text.shift(self.graph_origin+a1+0.2)).scale(.7)
+ vec2_text=(vec2_text.shift(self.graph_origin+a2+0.2)).scale(.7)
+ self.setup_axes(animate=True)
+ self.wait(2)
+ self.play(ShowCreation(vec1))
+ self.play(ShowCreation(vec1_text))
+ self.wait(.7)
+ self.play(ShowCreation(vec2))
+ self.play(ShowCreation(vec2_text))
+ self.wait(.7)
+ a=TextMobject(r"$\vec{a} = (1,2)$",color=RED_B).scale(.6)
+ a.shift(3*LEFT+2.7*UP)
+ b=TextMobject(r"$\vec{b} = (1,1)$",color=YELLOW_E).scale(.6)
+ b.shift(3*LEFT+2*UP)
+ self.play(ShowCreation(a))
+ self.play(ShowCreation(b))
+ self.wait(.5)
+ c=TextMobject(r"$2\cdot\vec{a} = 2\cdot(1,2) = (2,4)$",color=RED_B)
+ c.shift(3*LEFT+2.7*UP)
+ c.scale(.6)
+ self.play(Transform(a,c))
+ scaling1=TextMobject(r"Scaling vector $\vec{a}$ by 2 units",color=GOLD).scale(.5)
+ scaling1.shift(3.4*RIGHT+2.4*UP)
+ self.play(ShowCreation(scaling1))
+ a1=2*XD*RIGHT+4*YD*UP
+ self.play(FadeOut(vec1_text))
+ vec1_scaled=Vector(direction=a1).set_color(RED_E)
+ vec1_scaled.shift(self.graph_origin)
+ self.play(ShowCreation(vec1_scaled))
+ self.play(FadeOut(vec1))
+ vec1_scaled_text=TextMobject(r"$2\vec{a}$").scale(.7)
+ vec1_scaled_text.shift(self.graph_origin+a1+0.2)
+ self.play(ShowCreation(vec1_scaled_text))
+ self.play(FadeOut(scaling1))
+ d=TextMobject(r"$3\cdot\vec{b} = 3\cdot(1,1) = (3,3)$",color=YELLOW_E).scale(.6)
+ d.shift(3*LEFT+2*UP)
+ self.play(Transform(b,d))
+ scaling2=TextMobject(r"Scaling vector $\vec{b}$ by 3 units",color=GOLD).scale(.5)
+ scaling2.shift(3.4*RIGHT+2.4*UP)
+ self.play(ShowCreation(scaling2))
+ a2=3*XD*RIGHT+3*YD*UP
+ self.play(FadeOut(vec2_text))
+ vec2_2=Vector
+ vec2_scaled=Vector(direction=a2).set_color(YELLOW_E)
+ vec2_scaled.shift(self.graph_origin)
+ self.play(ShowCreation(vec2_scaled))
+ self.play(FadeOut(vec2))
+ vec2_scaled_text=TextMobject(r"$3\vec{b}$").scale(.7)
+ vec2_scaled_text.shift(self.graph_origin+a2+0.2)
+ self.play(ShowCreation(vec2_scaled_text))
+ self.wait(.7)
+ self.play(FadeOut(scaling2))
+ add = TextMobject("+").scale(.7)
+ add.shift(4.8*LEFT+2*UP)
+ self.play(ShowCreation(add))
+ self.wait(.5)
+ line = Line()
+ line.shift(3*LEFT+1.6*UP)
+ line.scale(1.8)
+ self.play(ShowCreation(line))
+ self.wait(1)
+ e = TextMobject(r"$\vec{c} = 2\cdot\vec{a} + 3\cdot\vec{b} = (5,7)$",color=GREEN_D).scale(.6)
+ e.shift(3*LEFT+1.3*UP)
+ self.play(ShowCreation(e))
+ self.wait(.5)
+ add1=TextMobject("Addition of the scaled vectors",color=GOLD).scale(.5)
+ add1.shift(4.1*RIGHT+2.4*UP)
+ self.play(ShowCreation(add1))
+ self.wait(.5)
+ self.play(FadeOut(vec1_scaled_text))
+ self.play(FadeOut(vec2_scaled_text))
+ self.play(FadeOut(vec1_scaled))
+ vec1_scaled2=Vector(direction=a1).set_color(RED_E)
+ vec1_scaled2.shift(self.graph_origin+3*RIGHT*XD+3*UP*YD)
+ self.play(ShowCreation(vec1_scaled2))
+ a3=5*XD*RIGHT+7*YD*UP
+ vec3=Vector(direction=a3).set_color(GREEN_C)
+ vec3.shift(self.graph_origin)
+ vec3_text=TextMobject(r"$\vec{c}$").scale(.7)
+ vec3_text.shift(self.graph_origin+a3+0.2)
+ self.play(ShowCreation(vec3))
+ self.wait(.5)
+ self.play(ShowCreation(vec3_text))
+ self.wait(1)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Space_As_Functions.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Space_As_Functions.py new file mode 100644 index 0000000..4f5614d --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Space_As_Functions.py @@ -0,0 +1,62 @@ +from manimlib.imports import *
+from scipy import sin,cos
+class FunctionalVectorSpace(GraphScene):
+ CONFIG = {
+ "x_min": -5,
+ "x_max": 5,
+ "y_min": -5,
+ "y_max": 5,
+ "graph_origin": ORIGIN,
+ }
+ def construct(self):
+ self.setup_axes(animate = True)
+ curve1 = self.get_graph(lambda x : sin(x), x_min=-5,x_max=5,color=YELLOW_E)
+ curve2 = self.get_graph(lambda x : cos(x), x_min=-5,x_max=5,color=RED)
+ self.play(ShowCreation(curve1))
+ fx=TextMobject(r"$f(x)$",color=YELLOW_E).scale(0.7)
+ fx.shift(5*LEFT+0.7*UP)
+ self.play(ShowCreation(fx))
+ self.play(ShowCreation(curve2))
+ gx=TextMobject(r"$g(x)$",color=RED).scale(0.7)
+ gx.shift(5*LEFT+0.2*UP)
+ self.play(ShowCreation(gx))
+ self.wait(2)
+ scaling=TextMobject("Scaling f(x) by 2 units",color=GOLD).scale(0.65)
+ scaling.shift(3*LEFT+2.4*UP)
+ curve3 = self.get_graph(lambda x : 2*sin(x), x_min=-5,x_max=5,color=BLUE)
+ fx2=TextMobject(r"$2f(x)$",color=BLUE).scale(0.7)
+ fx2.shift(5*LEFT+1*UP)
+ self.play(Transform(curve1,curve3),FadeOut(fx),ShowCreation(fx2),ShowCreation(scaling))
+ self.wait(3)
+ hx = TextMobject(r"$h(x)$",color=PURPLE).scale(0.7)
+ hx.shift(4.9*LEFT+1.5*UP)
+ curve4 = self.get_graph(lambda x : 2*sin(x) + cos(x), x_min=-5,x_max=5,color=PURPLE)
+ self.play(ShowCreation(curve4),ShowCreation(hx))
+ self.play(FadeOut(curve2),FadeOut(curve1),FadeOut(fx2),FadeOut(gx),FadeOut(scaling))
+ hxn=TextMobject(r"$h(x)$",color=PURPLE).scale(0.7)
+ hxn.shift(3*RIGHT+2.4*UP)
+ equal = TextMobject("=").scale(0.7)
+ equal.shift(3.5*RIGHT+2.4*UP)
+ fx2n=TextMobject(r"$2f(x)$",color=BLUE).scale(0.7)
+ fx2n.shift(4.2*RIGHT+2.4*UP)
+ add=TextMobject("+").scale(0.7)
+ add.shift(4.8*RIGHT+2.4*UP)
+ gxn=TextMobject(r"$g(x)$",color=RED).scale(0.7)
+ gxn.shift(5.3*RIGHT+2.4*UP)
+ vector_add=TextMobject("Vector Addition",color=GOLD).scale(0.65)
+ vector_add.shift(3*UP+3*RIGHT)
+ self.play(ShowCreation(hxn),ShowCreation(equal),ShowCreation(fx2n),ShowCreation(add),ShowCreation(gxn),ShowCreation(vector_add))
+ self.wait(2)
+
+
+
+
+
+
+
+
+
+
+
+
+
\ No newline at end of file diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/3D_Vector_Space.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/3D_Vector_Space.gif Binary files differnew file mode 100644 index 0000000..137546a --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/3D_Vector_Space.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Function_Vector_Space_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Function_Vector_Space_Example.gif Binary files differnew file mode 100644 index 0000000..d9edf46 --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Function_Vector_Space_Example.gif diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif Binary files differnew file mode 100644 index 0000000..ed65f8a --- /dev/null +++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif |
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