From a74eaef144ee85b1fd2fa0b39fcebad9fbc44190 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Mon, 6 Jul 2020 17:10:30 +0530
Subject: animation changed in 4FSS
---
.../The-Four-Fundamental-Subspaces/null_space.py | 91 ++++++++++++++++++++++
1 file changed, 91 insertions(+)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/null_space.py
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/null_space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/null_space.py
new file mode 100644
index 0000000..dfc3cb4
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/null_space.py
@@ -0,0 +1,91 @@
+from manimlib.imports import *
+class null_space(LinearTransformationScene):
+ def construct(self):
+
+ self.setup()
+ self.wait()
+
+ o = TextMobject(r"This is the original $2D$ vector space(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 particular vector $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$")
+ 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)
+ arrow1 = Arrow(start = ORIGIN, end = 2*(UP+RIGHT))
+ arrow2 = Arrow(start = ORIGIN, end = 3*(UP+RIGHT))
+ arrow3 = Arrow(start = ORIGIN, end = 4*(UP+RIGHT))
+ arrow4 = Arrow(start = ORIGIN, end = DOWN+LEFT)
+ arrow5 = Arrow(start = ORIGIN, end = 2*(DOWN+LEFT))
+ arrow6 = Arrow(start = ORIGIN, end = 3*(DOWN+LEFT))
+ arrow7 = Arrow(start = ORIGIN, end = 4*(DOWN+LEFT))
+
+ 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))
+
+ 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)
+
+ o1 = TextMobject("Notice, entire set of vectors which belong to the vector")
+ o2 = TextMobject(r"subspace(Linear Span of $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$) transforms to zero")
+ o1.move_to(2*DOWN+2.5*RIGHT)
+ o2.move_to(2.75*DOWN+2.5*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))
+ self.wait()
+
+ matrix = [[1,-1],[1,-1]]
+ self.apply_matrix(matrix)
+ self.wait()
+
+ self.play(FadeOut(o1), FadeOut(o2))
+
+ o = TextMobject(r"Hence, the vector space formed by linear span of $\left(\begin{array}{c} 1 \\ 1 \end{array}\right)$ is the null space of $A$")
+ o.move_to(DOWN)
+ o.scale(0.75)
+ o.add_background_rectangle()
+ self.play(Write(o))
+ self.wait(2)
+ self.play(FadeOut(o), FadeOut(arrow), FadeOut(arrow1), FadeOut(arrow2), FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(arrow6), FadeOut(arrow7))
--
cgit