2 files changed, 116 insertions, 0 deletions
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
new file mode 100755
index 0000000..b400f93
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
@@ -0,0 +1,34 @@
+from manimlib.imports import *
+
+class Orthogonal(ThreeDScene):
+    def construct(self):
+        axes = ThreeDAxes()
+        self.play(ShowCreation(axes))
+        self.move_camera(phi=30*DEGREES,theta=-45*DEGREES,run_time=3)
+        line1 = Line(start = ORIGIN,end = -3*LEFT)
+        line1.set_color(DARK_BLUE)
+        tip1 = Polygon(-LEFT,-0.8*LEFT-0.2*DOWN,-0.8*LEFT-0.2*UP)
+        tip1.move_to(-3*LEFT)
+        tip1.set_opacity(1)
+        tip1.set_fill(DARK_BLUE)
+        tip1.set_color(DARK_BLUE)
+
+        arrow2 = Line(start = ORIGIN,end = -3*UP)
+        arrow2.set_color(DARK_BLUE)
+        tip2 = Polygon(DOWN,0.8*DOWN-0.2*RIGHT,0.8*DOWN-0.2*LEFT)
+        tip2.move_to(3*DOWN)
+        tip2.set_opacity(1)
+        tip2.set_fill(DARK_BLUE)
+        tip2.set_color(DARK_BLUE)
+        arrow2.set_color(DARK_BLUE)
+
+        arrow3 = Line(start = ORIGIN,end = [0,0,3])
+        arrow3.set_color(DARK_BLUE)
+        tip3 = Polygon([0,0,3],[0,0,2.8]-0.2*RIGHT,[0,0,2.8]-0.2*LEFT)
+        tip3.set_opacity(1)
+        tip3.set_fill(DARK_BLUE)
+        tip3.set_color(DARK_BLUE)
+
+        self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3))
+        
+        self.wait()
+\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
new file mode 100644
index 0000000..0a28f22
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
@@ -0,0 +1,82 @@
+from manimlib.imports import *
+class OrthonormalBasis(GraphScene):
+    CONFIG = {
+        "x_min" : -6,
+        "x_max" : 6,
+        "y_min" : -4,
+        "y_max" : 4,
+        "graph_origin" : ORIGIN ,
+}
+
+    def construct(self):
+        self.setup_axes(animate=True)
+
+        XTD = self.x_axis_width/(self.x_max-self.x_min)
+        YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+        arrow1 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*RIGHT)
+        arrow1.scale(2.25)
+        arrow1.set_color(DARK_BLUE)
+
+        arrow2 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*LEFT)
+        arrow2.scale(2.25)
+        arrow2.set_color(DARK_BLUE)
+
+        square = Polygon(UP*0.4*YTD,0.2*(YTD*UP+XTD*RIGHT),ORIGIN,0.2*(YTD*UP+XTD*LEFT))
+        square.set_color(DARK_BLUE)
+        self.play(ShowCreation(arrow2), ShowCreation(arrow1), ShowCreation(square))
+
+        ortho = TextMobject("Orthonormal Vectors")
+        ortho.scale(0.75)
+        ortho.move_to(DOWN+3*RIGHT)
+        self.play(Write(ortho))
+        self.wait()
+        self.play(FadeOut(ortho))
+
+        arrow3 = Arrow(start = ORIGIN,end = YTD*3*UP+XTD*LEFT)
+        arrow3.scale(1.25)
+        arrow3.set_color(GOLD_E)
+        self.play(ShowCreation(arrow3))
+
+        arrow4 = Arrow(start = ORIGIN,end = YTD*UP+XTD*RIGHT)
+        arrow4.scale(1.8)
+        arrow4.set_color(GOLD_A)
+        
+        arrow5 = Arrow(start = ORIGIN,end = 2*YTD*UP-2*XTD*RIGHT)
+        arrow5.scale(1.3)
+        arrow5.set_color(GOLD_A)
+        
+        self.play(ShowCreation(arrow5), ShowCreation(arrow4))
+        
+        self.wait()
+
+        self.play(FadeOut(arrow1), FadeOut(arrow2), FadeOut(square))
+
+        self.wait()
+
+        text1 = TextMobject(r"$<v,v_1> v_1$")
+        text1.move_to(UP+2*RIGHT)
+        text1.scale(0.75)
+        text2 = TextMobject(r"$<v,v_2> v_2$")
+        text2.move_to(UP+3*LEFT)
+        text2.scale(0.75)
+        
+        text3 = TextMobject("v")
+        text3.move_to(YTD*3.5*UP+XTD*1.5*LEFT)
+
+        self.play(Write(text1), Write(text2), Write(text3))
+        self.wait()
+
+        line1 = DashedLine(start = YTD*UP+XTD*RIGHT, end = YTD*3*UP+XTD*1*LEFT)
+        line2 = DashedLine(start = YTD*2*UP+XTD*2*LEFT, end = YTD*3*UP+XTD*1*LEFT)
+        self.play(ShowCreation(line1),ShowCreation(line2))
+
+        self.wait()
+        
+        text = TextMobject(r"$v$ is the sum of projections","on the orthonormal vectors")
+        text[0].move_to(DOWN+3.2*RIGHT)
+        text[1].move_to(1.5*DOWN+3.2*RIGHT)
+        self.play(Write(text))
+        self.wait(2)
+        self.play(FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(text1), FadeOut(text2), FadeOut(text3), FadeOut(self.axes), FadeOut(line1), FadeOut(line2))
+        self.play(FadeOut(text))