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| author | Purusharth Saxena | 2020-06-23 18:06:56 +0530 |
|---|---|---|
| committer | GitHub | 2020-06-23 18:06:56 +0530 |
| commit | d0c1b826b41a0a0f93079b6ca755f2cef132ce6e (patch) | |
| tree | 6c851e4ea4e369c536bb183aa9378926b78dcee6 /FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem | |
| parent | a896e8b74b1b4864f24d860ea82e4de46d2ff2c7 (diff) | |
| parent | 959329ed76fb5350f5f68aeb8937a37b62138890 (diff) | |
| download | FSF-mathematics-python-code-archive-d0c1b826b41a0a0f93079b6ca755f2cef132ce6e.tar.gz FSF-mathematics-python-code-archive-d0c1b826b41a0a0f93079b6ca755f2cef132ce6e.tar.bz2 FSF-mathematics-python-code-archive-d0c1b826b41a0a0f93079b6ca755f2cef132ce6e.zip | |
Merge branch 'master' into master
Diffstat (limited to 'FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem')
| -rw-r--r-- | FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt | 3 | ||||
| -rwxr-xr-x | FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py | 97 |
2 files changed, 100 insertions, 0 deletions
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..5c48a13 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file.txt @@ -0,0 +1,3 @@ +file 'RN_Line.mp4' +file 'RN_Point.mp4' +file 'RN_SameDim.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..e54276c --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file1_RN_Theorem.py @@ -0,0 +1,97 @@ +from manimlib.imports import *
+class RN_Line(LinearTransformationScene):
+ def construct(self):
+
+ self.setup()
+ self.wait()
+
+ predim = TextMobject("Dimension of this vector space is 2")
+ predim.move_to(DOWN+4*LEFT)
+ predim.scale(0.75)
+ predim.add_background_rectangle()
+ 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)
+ afterlt.add_background_rectangle()
+
+ afterlt2 = TextMobject("Dimension of the vector space","changes to 1")
+ afterlt2[0].move_to(1.5*DOWN+4*LEFT)
+ afterlt2[1].move_to(2*DOWN+4*LEFT)
+ afterlt2.scale(0.75)
+ afterlt2.add_background_rectangle()
+ 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))
+
+class RN_Point(LinearTransformationScene):
+ def construct(self):
+ self.setup()
+ self.wait()
+ predim = TextMobject("Another One")
+ predim.move_to(DOWN+4*LEFT)
+ predim.scale(0.75)
+ predim.add_background_rectangle()
+ 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)
+ afterlt.add_background_rectangle()
+ afterlt2 = TextMobject("Dimension of the vector space","changes to 0")
+ afterlt2[0].move_to(1.5*DOWN+4*LEFT)
+ afterlt2[1].move_to(2*DOWN+4*LEFT)
+ afterlt2.scale(0.75)
+ afterlt2.add_background_rectangle()
+ 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)
+ self.play(FadeOut(afterlt),FadeOut(afterlt2),Write(nullity))
+ self.wait(1)
+ self.play(FadeOut(nullity))
+
+class RN_SameDim(LinearTransformationScene):
+ def construct(self):
+ self.setup()
+ self.wait()
+ predim = TextMobject("Let us look at another example")
+ predim.add_background_rectangle()
+ 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)
+ afterlt.add_background_rectangle()
+ afterlt2 = TextMobject("Dimension of the vector space","remains to be 2")
+ afterlt2[0].move_to(1.5*DOWN+4*LEFT)
+ afterlt2[1].move_to(2*DOWN+4*LEFT)
+ afterlt2.scale(0.75)
+ afterlt2.add_background_rectangle()
+ 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))
\ No newline at end of file |