From 5d7d773aadf04a88b3238853c60a2ea1217804b2 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Wed, 10 Jun 2020 09:05:58 +0530
Subject: Rank Nullity Theorem

---
 .../The-Rank-Nullity-Theorem/file.txt              |  2 +
 .../The-Rank-Nullity-Theorem/file1_RN_Theorem.py   | 58 ++++++++++++++++++++++
 .../The-Rank-Nullity-Theorem/file2_RN_Theorem1.py  | 33 ++++++++++++
 3 files changed, 93 insertions(+)
 create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
 create mode 100755 FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
 create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2_RN_Theorem1.py

(limited to 'FSF-2020')

diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
new file mode 100644
index 0000000..890fe45
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt
@@ -0,0 +1,2 @@
+file 'RN_Theorem.mp4'
+file 'RN_Theorem1.mp4'
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
new file mode 100755
index 0000000..31330e2
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py
@@ -0,0 +1,58 @@
+from manimlib.imports import *
+class RN_Theorem(LinearTransformationScene):
+    def construct(self):
+        self.setup()
+        self.wait()
+        square = Square(fill_color=BLACK, fill_opacity=1,color = BLUE)
+        square.move_to(4*LEFT+4*DOWN)
+        square.scale(4)
+        self.play(ShowCreation(square))
+        predim = TextMobject("Dimension of this vector space is 2")
+        predim.move_to(DOWN+4*LEFT)
+        predim.scale(0.75)
+        self.play(Write(predim))
+        self.wait()
+        self.play(FadeOut(predim))
+        afterlt = TextMobject("After Linear transformation")
+        afterlt.move_to(DOWN+4*LEFT)
+        afterlt.scale(0.75)
+        afterlt2 = TextMobject("Dimension of the vector space","remains to be 2")
+        afterlt2[0].move_to(2*DOWN+4*LEFT)
+        afterlt2[1].move_to(3*DOWN+4*LEFT)
+        afterlt2.scale(0.75)
+        matrix = [[1,1],[0,1]]
+        self.apply_matrix(matrix)
+        self.play(Write(afterlt))
+        self.play(Write(afterlt2))
+        self.wait()
+        nullity = TextMobject("Hence, nullity = 0")
+        nullity.move_to(DOWN+4*LEFT)
+        self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
+        self.wait(1)
+        self.play(FadeOut(nullity))
+
+        predim = TextMobject("Let us look at another example")
+        predim.move_to(DOWN+4*LEFT)
+        predim.scale(0.75)
+        matrix = [[1,-1],[0,1]]
+        self.apply_matrix(matrix)
+        self.play(Write(predim))
+        self.wait()
+        self.play(FadeOut(predim))
+        afterlt = TextMobject("After Linear transformation")
+        afterlt.move_to(DOWN+4*LEFT)
+        afterlt.scale(0.75)
+        afterlt2 = TextMobject("Dimension of the vector space","changes to 1")
+        afterlt2[0].move_to(2*DOWN+4*LEFT)
+        afterlt2[1].move_to(3*DOWN+4*LEFT)
+        afterlt2.scale(0.75)
+        matrix = [[1,1],[1,1]]
+        self.apply_matrix(matrix)
+        self.play(Write(afterlt))
+        self.play(Write(afterlt2))
+        self.wait()
+        nullity = TextMobject("Hence, nullity = 1")
+        nullity.move_to(DOWN+4*LEFT)
+        self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
+        self.wait(1)
+        self.play(FadeOut(nullity))
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2_RN_Theorem1.py b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2_RN_Theorem1.py
new file mode 100644
index 0000000..8f05ddd
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2_RN_Theorem1.py
@@ -0,0 +1,33 @@
+from manimlib.imports import *
+class RN_Theorem1(LinearTransformationScene):
+    def construct(self):
+        self.setup()
+        self.wait()
+        square = Square(fill_color=BLACK, fill_opacity=1,color = BLUE)
+        square.move_to(4*LEFT+4*DOWN)
+        square.scale(4)
+        self.play(ShowCreation(square))
+        predim = TextMobject("Another One")
+        predim.move_to(DOWN+4*LEFT)
+        predim.scale(0.75)
+        self.play(Write(predim))
+        self.wait()
+        self.play(FadeOut(predim))
+        afterlt = TextMobject("After Linear transformation")
+        afterlt.move_to(DOWN+4*LEFT)
+        afterlt.scale(0.75)
+        afterlt2 = TextMobject("Dimension of the vector space","changes to 0")
+        afterlt2[0].move_to(2*DOWN+4*LEFT)
+        afterlt2[1].move_to(3*DOWN+4*LEFT)
+        afterlt2.scale(0.75)
+        matrix = [[0,0],[0,0]]
+        self.apply_matrix(matrix)
+        self.play(Write(afterlt))
+        self.play(Write(afterlt2))
+        self.wait()
+        nullity = TextMobject("Hence, nullity = 2")
+        nullity.move_to(DOWN+4*LEFT)
+        #afterlt.scale(0.75)
+        self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
+        self.wait(1)
+        self.play(FadeOut(nullity))
-- 
cgit