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A few cleanup chapter10 animations
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Grant Sanderson
parent
2ec1db94d0
commit
82143e2d64
1 changed files with 131 additions and 7 deletions
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@ -644,6 +644,15 @@ class DeduceTransformationFromMatrix(ColumnsToBasisVectors):
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def construct(self):
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self.setup()
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self.move_matrix_columns([[3, 0], [1, 2]])
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words = TextMobject("""
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This gives too much weight
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to our coordinate system
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""")
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words.add_background_rectangle()
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words.next_to(ORIGIN, DOWN+LEFT, buff = MED_BUFF)
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words.shift_onto_screen()
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self.play(Write(words))
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self.dither()
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class WordsOnComputation(TeacherStudentsScene):
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def construct(self):
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@ -1204,7 +1213,7 @@ class LineOfReasoning(Scene):
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class IfYouDidntKnowDeterminants(TeacherStudentsScene):
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def construct(self):
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expression = TexMobject("\\det(A-", "\\lambda", ")=0")
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expression = TexMobject("\\det(A-", "\\lambda", "I" ")=0")
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expression.highlight_by_tex("\\lambda", MAROON_B)
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expression.scale(1.3)
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self.teacher_says(expression)
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@ -1758,6 +1767,16 @@ class ShearExample(RevisitExampleTransformation):
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# self.lambda_equals_two = lambda_equals_two
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# self.dither()
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class EigenvalueCanHaveMultipleEigenVectors(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("""
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A single eigenvalue can
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have more that a line
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full of eigenvectors
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""")
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self.change_student_modes(*["pondering"]*3)
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self.random_blink(2)
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class ScalingExample(LinearTransformationScene):
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CONFIG = {
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"t_matrix" : [[2, 0], [0, 2]]
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@ -1925,6 +1944,74 @@ class DefineDiagonalMatrix(Scene):
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)
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self.dither()
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class RepeatedMultiplicationInAction(Scene):
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def construct(self):
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vector = Matrix(["x", "y"])
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vector.highlight(YELLOW)
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vector.scale(1.2)
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vector.shift(RIGHT)
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matrix, scalars = self.get_matrix(vector)
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#First multiplication
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for v_entry, scalar in zip(vector.get_entries(), scalars):
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scalar.target = scalar.copy()
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scalar.target.next_to(v_entry, LEFT)
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l_bracket = vector.get_brackets()[0]
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l_bracket.target = l_bracket.copy()
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l_bracket.target.next_to(VGroup(*[
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scalar.target for scalar in scalars
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]), LEFT)
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self.add(vector)
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self.play(*map(FadeIn, [matrix]+scalars))
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self.dither()
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self.play(
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FadeOut(matrix),
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*map(MoveToTarget, scalars + [l_bracket])
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)
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self.dither()
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#nth multiplications
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for scalar in scalars:
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scalar.exp = VectorizedPoint(scalar.get_corner(UP+RIGHT))
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scalar.exp.shift(SMALL_BUFF*RIGHT/2.)
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for new_exp in range(2, 6):
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matrix, new_scalars = self.get_matrix(vector)
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new_exp_mob = TexMobject(str(new_exp)).scale(0.7)
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movers = []
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to_remove = []
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for v_entry, scalar, new_scalar in zip(vector.get_entries(), scalars, new_scalars):
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scalar.exp.target = new_exp_mob.copy()
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scalar.exp.target.highlight(scalar.get_color())
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scalar.exp.target.move_to(scalar.exp, aligned_edge = LEFT)
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new_scalar.target = scalar.exp.target
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scalar.target = scalar.copy()
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VGroup(scalar.target, scalar.exp.target).next_to(
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v_entry, LEFT, aligned_edge = DOWN
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)
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movers += [scalar, scalar.exp, new_scalar]
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to_remove.append(new_scalar)
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l_bracket.target.next_to(VGroup(*[
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scalar.target for scalar in scalars
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]), LEFT)
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movers.append(l_bracket)
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self.play(*map(FadeIn, [matrix]+new_scalars))
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self.dither()
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self.play(
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FadeOut(matrix),
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*map(MoveToTarget, movers)
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)
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self.remove(*to_remove)
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self.dither()
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def get_matrix(self, vector):
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matrix = Matrix([[3, 0], [0, 2]])
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matrix.highlight_columns(X_COLOR, Y_COLOR)
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matrix.next_to(vector, LEFT)
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scalars = [matrix.get_mob_matrix()[i, i] for i in range(2)]
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matrix.remove(*scalars)
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return matrix, scalars
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class RepeatedMultilpicationOfMatrices(Scene):
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CONFIG = {
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"matrix" : [[3, 0], [0, 2]],
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@ -2007,9 +2094,27 @@ class WhatAreTheOddsOfThat(TeacherStudentsScene):
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self.change_student_modes("pondering")
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self.random_blink(3)
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class LastVideo(Scene):
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def construct(self):
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title = TextMobject("Last chapter: Change of basis")
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title.to_edge(UP)
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rect = Rectangle(width = 16, height = 9, color = BLUE)
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rect.scale_to_fit_height(6)
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rect.next_to(title, DOWN, buff = MED_BUFF)
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self.add(title)
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self.play(ShowCreation(rect))
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self.dither()
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class ChangeToEigenBasis(ExampleTranformationScene):
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CONFIG = {
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"show_basis_vectors" : False
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"show_basis_vectors" : False,
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"include_background_plane" : False,
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"foreground_plane_kwargs" : {
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"x_radius" : 2*SPACE_WIDTH,
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"y_radius" : 2*SPACE_HEIGHT,
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"secondary_line_ratio" : 0
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},
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}
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def construct(self):
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self.plane.fade()
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@ -2116,7 +2221,7 @@ class ChangeToEigenBasis(ExampleTranformationScene):
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neg_1 = TexMobject("-1")
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neg_1.add_background_rectangle()
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inv_cob.target.next_to(
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self.matrix, LEFT, buff = neg_1.get_width()+SMALL_BUFF
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self.matrix, LEFT, buff = neg_1.get_width()+2*SMALL_BUFF
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)
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neg_1.next_to(
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inv_cob.target.get_corner(UP+RIGHT),
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@ -2130,6 +2235,16 @@ class ChangeToEigenBasis(ExampleTranformationScene):
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self.add_foreground_mobject(cob_matrix, inv_cob, neg_1)
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self.play(*map(FadeOut, self.to_fade))
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self.dither()
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self.play(FadeOut(self.plane))
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cob_transform = self.get_matrix_transformation([[1, 0], [-1, 1]])
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ApplyMethod(self.plane.apply_function, cob_transform).update(1)
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self.plane.main_lines.highlight(BLUE_D)
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self.plane.axes.highlight(WHITE)
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self.play(
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FadeIn(self.plane),
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*map(Animation, self.foreground_mobjects+self.moving_vectors)
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)
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self.add(self.plane.copy().highlight(GREY).set_stroke(width = 2))
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self.apply_transposed_matrix(self.t_matrix)
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equals = TexMobject("=").next_to(cob_matrix)
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@ -2146,14 +2261,16 @@ class ChangeToEigenBasis(ExampleTranformationScene):
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eigenbasis = TextMobject("``Eigenbasis''")
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eigenbasis.add_background_rectangle()
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eigenbasis.next_to(ORIGIN, DOWN+LEFT)
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eigenbasis.next_to(ORIGIN, DOWN)
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self.play(Write(eigenbasis))
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self.dither()
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def ask_about_power(self):
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morty = Mortimer()
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morty.to_corner(DOWN+RIGHT)
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bubble = morty.get_bubble("speech", height = 3, width = 5)
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morty.to_edge(DOWN).shift(LEFT)
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bubble = morty.get_bubble(
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"speech", height = 3, width = 5, direction = RIGHT
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)
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bubble.set_fill(BLACK, opacity = 1)
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matrix_copy = self.matrix.copy().scale(0.7)
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hundred = TexMobject("100").scale(0.7)
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@ -2173,7 +2290,14 @@ class ChangeToEigenBasis(ExampleTranformationScene):
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self.play(Blink(morty))
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self.dither(2)
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class CannotDoWithWithAllTransformations(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("""
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Not all matrices
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can become diagonal
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""")
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self.change_student_modes(*["tired"]*3)
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self.random_blink(2)
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