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from manimlib.imports import *
class row_space(LinearTransformationScene):
def construct(self):
self.setup()
self.wait()
o = TextMobject(r"This is the original vector space $R^2$(before Linear Transformation)")
o.move_to(DOWN)
o.scale(0.75)
o.add_background_rectangle()
self.play(Write(o))
self.wait()
self.play(FadeOut(o))
o1 = TextMobject("Consider a set of vectors which are linear")
o2 = TextMobject(r"span of a $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$i.e. the null space.")
o1.move_to(2*DOWN+3*RIGHT)
o2.move_to(2.75*DOWN+3*RIGHT)
o1.scale(0.7)
o2.scale(0.7)
o1.add_background_rectangle()
o2.add_background_rectangle()
self.play(Write(o1))
self.play(Write(o2))
arrow = Arrow(start = ORIGIN, end = UP+RIGHT)
arrow.set_color(YELLOW)
arrow1 = Arrow(start = ORIGIN, end = 2*(UP+RIGHT))
arrow1.set_color(YELLOW)
arrow2 = Arrow(start = ORIGIN, end = 3*(UP+RIGHT))
arrow2.set_color(YELLOW)
arrow3 = Arrow(start = ORIGIN, end = 4*(UP+RIGHT))
arrow3.set_color(YELLOW)
arrow4 = Arrow(start = ORIGIN, end = DOWN+LEFT)
arrow4.set_color(YELLOW)
arrow5 = Arrow(start = ORIGIN, end = 2*(DOWN+LEFT))
arrow5.set_color(YELLOW)
arrow6 = Arrow(start = ORIGIN, end = 3*(DOWN+LEFT))
arrow6.set_color(YELLOW)
arrow7 = Arrow(start = ORIGIN, end = 4*(DOWN+LEFT))
arrow7.set_color(YELLOW)
arrow.scale(1.5)
arrow1.scale(1.2)
arrow2.scale(1.15)
arrow3.scale(1.1)
arrow4.scale(1.5)
arrow5.scale(1.2)
arrow6.scale(1.15)
arrow7.scale(1.1)
self.play(ShowCreation(arrow),
ShowCreation(arrow1),
ShowCreation(arrow2),
ShowCreation(arrow3),
ShowCreation(arrow4),
ShowCreation(arrow5),
ShowCreation(arrow6),
ShowCreation(arrow7),
)
self.wait(2)
self.play(FadeOut(o1), FadeOut(o2))
o1 = TextMobject("Consider a set of vectors which are linear")
o2 = TextMobject(r"span of a vector $\left(\begin{array}{c} 1 \\ -1 \end{array}\right)$i.e. the row space.")
o1.move_to(2*DOWN+3*RIGHT)
o2.move_to(2.75*DOWN+3*RIGHT)
o1.scale(0.7)
o2.scale(0.7)
o1.add_background_rectangle()
o2.add_background_rectangle()
self.play(Write(o1))
self.play(Write(o2))
rarrow = Arrow(start = ORIGIN, end = -UP+RIGHT)
rarrow.set_color(PURPLE)
rarrow1 = Arrow(start = ORIGIN, end = 2*(-UP+RIGHT))
rarrow1.set_color(PURPLE)
rarrow2 = Arrow(start = ORIGIN, end = 3*(-UP+RIGHT))
rarrow2.set_color(PURPLE)
rarrow3 = Arrow(start = ORIGIN, end = 4*(-UP+RIGHT))
rarrow3.set_color(PURPLE)
rarrow4 = Arrow(start = ORIGIN, end = -DOWN+LEFT)
rarrow4.set_color(PURPLE)
rarrow5 = Arrow(start = ORIGIN, end = 2*(-DOWN+LEFT))
rarrow5.set_color(PURPLE)
rarrow6 = Arrow(start = ORIGIN, end = 3*(-DOWN+LEFT))
rarrow6.set_color(PURPLE)
rarrow7 = Arrow(start = ORIGIN, end = 4*(-DOWN+LEFT))
rarrow7.set_color(PURPLE)
rarrow.scale(1.5)
rarrow1.scale(1.2)
rarrow2.scale(1.15)
rarrow3.scale(1.1)
rarrow4.scale(1.5)
rarrow5.scale(1.2)
rarrow6.scale(1.15)
rarrow7.scale(1.1)
self.play(ShowCreation(rarrow),
ShowCreation(rarrow1),
ShowCreation(rarrow2),
ShowCreation(rarrow3),
ShowCreation(rarrow4),
ShowCreation(rarrow5),
ShowCreation(rarrow6),
ShowCreation(rarrow7),
)
self.wait(2)
self.play(FadeOut(o1), FadeOut(o2))
self.add_transformable_mobject(arrow)
self.add_transformable_mobject(arrow1)
self.add_transformable_mobject(arrow2)
self.add_transformable_mobject(arrow3)
self.add_transformable_mobject(arrow4)
self.add_transformable_mobject(arrow5)
self.add_transformable_mobject(arrow6)
self.add_transformable_mobject(arrow7)
self.add_transformable_mobject(rarrow)
self.add_transformable_mobject(rarrow1)
self.add_transformable_mobject(rarrow2)
self.add_transformable_mobject(rarrow3)
self.add_transformable_mobject(rarrow4)
self.add_transformable_mobject(rarrow5)
self.add_transformable_mobject(rarrow6)
self.add_transformable_mobject(rarrow7)
matrix = [[1,-1],[1,-1]]
self.apply_matrix(matrix)
self.wait(3)
o1 = TextMobject("Consider a set of vectors which are linear span of a vector")
o2 = TextMobject(r"$\left(\begin{array}{c} 1 \\ -1 \end{array}\right)$ which is orthogonal to column space i.e. Left Null Space")
o1.move_to(2*DOWN)
o2.move_to(2.75*DOWN)
o1.scale(0.7)
o2.scale(0.7)
o1.add_background_rectangle()
o2.add_background_rectangle()
self.play(Write(o1))
self.play(Write(o2))
rarrow = Arrow(start = ORIGIN, end = -UP+RIGHT)
rarrow.set_color(YELLOW)
rarrow1 = Arrow(start = ORIGIN, end = 2*(-UP+RIGHT))
rarrow1.set_color(YELLOW)
rarrow2 = Arrow(start = ORIGIN, end = 3*(-UP+RIGHT))
rarrow2.set_color(YELLOW)
rarrow3 = Arrow(start = ORIGIN, end = 4*(-UP+RIGHT))
rarrow3.set_color(YELLOW)
rarrow4 = Arrow(start = ORIGIN, end = -DOWN+LEFT)
rarrow4.set_color(YELLOW)
rarrow5 = Arrow(start = ORIGIN, end = 2*(-DOWN+LEFT))
rarrow5.set_color(YELLOW)
rarrow6 = Arrow(start = ORIGIN, end = 3*(-DOWN+LEFT))
rarrow6.set_color(YELLOW)
rarrow7 = Arrow(start = ORIGIN, end = 4*(-DOWN+LEFT))
rarrow7.set_color(YELLOW)
rarrow.scale(1.5)
rarrow1.scale(1.2)
rarrow2.scale(1.15)
rarrow3.scale(1.1)
rarrow4.scale(1.5)
rarrow5.scale(1.2)
rarrow6.scale(1.15)
rarrow7.scale(1.1)
self.play(ShowCreation(rarrow),
ShowCreation(rarrow1),
ShowCreation(rarrow2),
ShowCreation(rarrow3),
ShowCreation(rarrow4),
ShowCreation(rarrow5),
ShowCreation(rarrow6),
ShowCreation(rarrow7),
)
self.wait(2)
self.play(FadeOut(o1), FadeOut(o2))
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