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from manimlib.imports import *
class LinearTrans(LinearTransformationScene):
CONFIG = {
"show_basis_vectors": True,
"basis_vector_stroke_width": 1,
"leave_ghost_vectors": False,
"show_coordinates": True,
}
def construct(self):
self.setup()
matrix = [[0.6,-0.8],[0.8,0.6]]
self.apply_matrix(matrix)
self.wait(2)
orthonormal = TextMobject(r"These are 2 orthonormal vectors($v_1$ and $v_2$)")
orthonormal.scale(0.7)
orthonormal.move_to(DOWN+LEFT*3.5)
orthonormal.add_background_rectangle()
v1 = TextMobject(r"$v_1$")
v1.scale(0.75)
v1.set_color(X_COLOR)
v1.move_to(0.75*UP+RIGHT)
v1.add_background_rectangle()
v2 = TextMobject(r"$v_2$")
v2.scale(0.75)
v2.set_color(Y_COLOR)
v2.move_to(0.75*UP+LEFT*1.25)
v2.add_background_rectangle()
self.play(Write(orthonormal))
self.play(Write(v1),Write(v2))
self.wait()
self.play(FadeOut(orthonormal), FadeOut(v1), FadeOut(v2))
arrow = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
arrow.scale(1.2)
arrow.set_color(BLUE)
arrow.apply_matrix(matrix)
text3 = TextMobject("v")
text3.move_to(3.2*UP+1.2*RIGHT)
text3.add_background_rectangle()
self.play(ShowCreation(arrow),Write(text3))
self.wait()
v_cor = TextMobject("(1 , 3)")
v_cor.move_to(3.2*UP+1.3*RIGHT)
v_cor.set_color(BLUE)
v_cor.scale(0.75)
v_cor.add_background_rectangle()
self.play(Transform(text3,v_cor))
line1 = DashedLine(start = 1*UP+3*RIGHT, end = 3*RIGHT)
line2 = DashedLine(start = 1*UP+3*RIGHT, end = UP)
line1.apply_matrix(matrix)
line2.apply_matrix(matrix)
self.play(ShowCreation(line1),ShowCreation(line2),run_time = 2)
v1 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
v1.scale(1.2)
v1.set_color(BLUE)
v1.apply_matrix(matrix)
arrow1 = Arrow(start = ORIGIN,end = 3*RIGHT)
arrow1.scale(1.2)
arrow1.set_color("#6B8E23")
arrow1.apply_matrix(matrix)
self.play(Transform(v1,arrow1))
v1_cor = TextMobject(r"$<v,v_1> v_1$")
v1_cor.move_to(2.5*UP+3*RIGHT)
v1_cor.scale(0.75)
v1_cor.add_background_rectangle()
self.play(Write(v1_cor))
self.wait(0.5)
text1 = TextMobject("(1.8 , 2.4)")
text1.move_to(2.1*UP+2.5*RIGHT)
text1.scale(0.75)
text1.set_color("#6B8E23")
text1.add_background_rectangle()
self.play(Transform(v1_cor,text1))
v2 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
v2.scale(1.2)
v2.set_color("#8b0000")
v2.apply_matrix(matrix)
arrow2 = Arrow(start = ORIGIN,end = UP)
arrow2.scale(2.1)
arrow2.set_color("#8b0000")
arrow2.apply_matrix(matrix)
self.wait(0.5)
self.play(Transform(v2,arrow2))
self.wait(0.5)
v2_cor = TextMobject(r"$<v,v_2> v_2$")
v2_cor.move_to(0.75*UP+2.5*LEFT)
v2_cor.scale(0.75)
v2_cor.add_background_rectangle()
self.play(Write(v2_cor))
self.wait(0.5)
text2 = TextMobject("(-0.8 , 0.6)")
text2.move_to(0.75*UP+1.75*LEFT)
text2.scale(0.75)
text2.set_color("#8b0000")
text2.add_background_rectangle()
self.play(Transform(v2_cor,text2))
self.wait()
self.play(ApplyMethod(v2.move_to,1.4*RIGHT+2.7*UP),FadeOut(v1_cor),FadeOut(v2_cor),FadeOut(v_cor))
self.wait()
ending = TextMobject(r"$v = <v,v_1> v_1 + <v,v_2> v_2$")
ending.scale(0.7)
ending.move_to(DOWN)
ending.add_background_rectangle()
self.play(Write(ending))
self.wait()
self.play(FadeOut(ending))
ending = TextMobject(r"$\left[ \begin{array} {c} 1\\ 3 \end{array}\right] = \left[ \begin{array} {c}1.8 \\ 2.4 \end{array}\right] + \left[ \begin{array} {c} -0.8\\ 0.6 \end{array}\right]$")
ending.scale(0.7)
ending.move_to(DOWN)
ending.add_background_rectangle()
self.play(Write(ending))
self.wait()
self.play(FadeOut(ending))
ending = TextMobject(r"$v$ is the sum of projections on the orthonormal vectors")
ending.scale(0.7)
ending.move_to(DOWN)
ending.add_background_rectangle()
self.play(Write(ending))
self.wait()
self.play(FadeOut(ending))
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