diff options
Diffstat (limited to 'FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/row_space.py')
| -rw-r--r-- | FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/row_space.py | 150 |
1 files changed, 150 insertions, 0 deletions
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/row_space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/row_space.py new file mode 100644 index 0000000..c81d370 --- /dev/null +++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/row_space.py @@ -0,0 +1,150 @@ +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 $\left(\begin{array}{c} 1 \\ -1 \end{array}\right)$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) + + o1 = TextMobject("Notice, entire set of vectors which belong to the null space of $A$ transforms to zero") + o2 = TextMobject(r"and entire set of vectors which belong to the row space of $A$ transforms to column space of $A$.") + o1.move_to(2.5*DOWN) + o2.move_to(3.5*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)) + self.wait() + + matrix = [[1,-1],[1,-1]] + self.apply_matrix(matrix) + self.wait(3) + + self.play(FadeOut(o1), FadeOut(o2))
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