1 files changed, 91 insertions, 0 deletions
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))