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3 files changed, 213 insertions, 0 deletions

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/3D_Vector_Space.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/3D_Vector_Space.py
new file mode 100644
index 0000000..70913eb
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/3D_Vector_Space.py
@@ -0,0 +1,14 @@
+from manimlib.imports import *

+class ThreeDSpace(ThreeDScene):

+	def construct(self):

+		curve = ParametricFunction(

+			lambda x:  np.array([

+		    0, -x , x]), color = YELLOW, t_min = -2, t_max = 2)

+		axes = ThreeDAxes()

+		axes.set_stroke(width=1,color=GOLD)		

+		self.add(axes)

+		self.set_camera_orientation(phi = 70*DEGREES,theta =60*DEGREES)

+		self.begin_ambient_camera_rotation(rate=0.3)

+		self.play(ShowCreation(curve))

+		self.wait(6)			

+		

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py
new file mode 100644
index 0000000..70af123
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py
@@ -0,0 +1,137 @@
+from manimlib.imports import *

+import numpy as np

+

+class vectorspace(GraphScene):

+	CONFIG={

+	"x_min": -7,

+	"x_max": 7,

+	"y_min": -7,

+	"y_max": 7,

+	"graph_origin": ORIGIN,

+	"x_axis_label":"$X$",

+	"y_axis_label":"$Y$",

+	"x_labeled_nums": list(np.arange(-7, 8,1)),

+	"y_labeled_nums": list(np.arange(-7, 8,1)),

+	"x_axis_width": 8,

+	"y_axis_height": 7,

+	"x_tick_frequency":1,

+	"axes_color": GREY,

+	"area_opacity": 3,

+    "num_rects": 10,

+	}	

+	def construct(self):

+		XD = self.x_axis_width/(self.x_max- self.x_min)

+		YD = self.y_axis_height/(self.y_max- self.y_min)	

+		a1=1*XD*RIGHT+2*YD*UP

+		a2=1*XD*RIGHT+1*YD*UP	

+		vec1=Vector(direction=a1).set_color(RED_E)

+		vec1.shift(self.graph_origin)

+		vec2=Vector(direction=a2).set_color(YELLOW_E)

+		vec2.shift(self.graph_origin)

+		vec1_text=TextMobject(r"$\vec{a}$")

+		vec2_text=TextMobject(r"$\vec{b}$")

+		vec1_text=(vec1_text.shift(self.graph_origin+a1+0.2)).scale(.7)

+		vec2_text=(vec2_text.shift(self.graph_origin+a2+0.2)).scale(.7)

+		self.setup_axes(animate=True)

+		self.wait(2)

+		self.play(ShowCreation(vec1))

+		self.play(ShowCreation(vec1_text))

+		self.wait(.7)

+		self.play(ShowCreation(vec2))

+		self.play(ShowCreation(vec2_text))

+		self.wait(.7)

+		a=TextMobject(r"$\vec{a} = (1,2)$",color=RED_B).scale(.6)

+		a.shift(3*LEFT+2.7*UP)

+		b=TextMobject(r"$\vec{b} = (1,1)$",color=YELLOW_E).scale(.6)

+		b.shift(3*LEFT+2*UP)

+		self.play(ShowCreation(a))

+		self.play(ShowCreation(b))

+		self.wait(.5)

+		c=TextMobject(r"$2\cdot\vec{a} = 2\cdot(1,2) = (2,4)$",color=RED_B)

+		c.shift(3*LEFT+2.7*UP)

+		c.scale(.6)

+		self.play(Transform(a,c))

+		scaling1=TextMobject(r"Scaling vector $\vec{a}$ by 2 units",color=GOLD).scale(.5)

+		scaling1.shift(3.4*RIGHT+2.4*UP)

+		self.play(ShowCreation(scaling1))

+		a1=2*XD*RIGHT+4*YD*UP

+		self.play(FadeOut(vec1_text))

+		vec1_scaled=Vector(direction=a1).set_color(RED_E)

+		vec1_scaled.shift(self.graph_origin)

+		self.play(ShowCreation(vec1_scaled))

+		self.play(FadeOut(vec1))

+		vec1_scaled_text=TextMobject(r"$2\vec{a}$").scale(.7)		

+		vec1_scaled_text.shift(self.graph_origin+a1+0.2)

+		self.play(ShowCreation(vec1_scaled_text))

+		self.play(FadeOut(scaling1))

+		d=TextMobject(r"$3\cdot\vec{b} = 3\cdot(1,1) = (3,3)$",color=YELLOW_E).scale(.6)

+		d.shift(3*LEFT+2*UP)

+		self.play(Transform(b,d))

+		scaling2=TextMobject(r"Scaling vector $\vec{b}$ by 3 units",color=GOLD).scale(.5)

+		scaling2.shift(3.4*RIGHT+2.4*UP)

+		self.play(ShowCreation(scaling2))

+		a2=3*XD*RIGHT+3*YD*UP

+		self.play(FadeOut(vec2_text))

+		vec2_2=Vector

+		vec2_scaled=Vector(direction=a2).set_color(YELLOW_E)

+		vec2_scaled.shift(self.graph_origin)

+		self.play(ShowCreation(vec2_scaled))

+		self.play(FadeOut(vec2))

+		vec2_scaled_text=TextMobject(r"$3\vec{b}$").scale(.7)

+		vec2_scaled_text.shift(self.graph_origin+a2+0.2)

+		self.play(ShowCreation(vec2_scaled_text))

+		self.wait(.7)

+		self.play(FadeOut(scaling2))

+		add = TextMobject("+").scale(.7)

+		add.shift(4.8*LEFT+2*UP)

+		self.play(ShowCreation(add))

+		self.wait(.5)

+		line = Line()

+		line.shift(3*LEFT+1.6*UP)

+		line.scale(1.8)

+		self.play(ShowCreation(line))

+		self.wait(1)

+		e = TextMobject(r"$\vec{c} = 2\cdot\vec{a} + 3\cdot\vec{b} = (5,7)$",color=GREEN_D).scale(.6)

+		e.shift(3*LEFT+1.3*UP)

+		self.play(ShowCreation(e))

+		self.wait(.5)

+		add1=TextMobject("Addition of the scaled vectors",color=GOLD).scale(.5)

+		add1.shift(4.1*RIGHT+2.4*UP)

+		self.play(ShowCreation(add1))

+		self.wait(.5)

+		self.play(FadeOut(vec1_scaled_text))

+		self.play(FadeOut(vec2_scaled_text))

+		self.play(FadeOut(vec1_scaled))

+		vec1_scaled2=Vector(direction=a1).set_color(RED_E)

+		vec1_scaled2.shift(self.graph_origin+3*RIGHT*XD+3*UP*YD)

+		self.play(ShowCreation(vec1_scaled2))

+		a3=5*XD*RIGHT+7*YD*UP	

+		vec3=Vector(direction=a3).set_color(GREEN_C)

+		vec3.shift(self.graph_origin)

+		vec3_text=TextMobject(r"$\vec{c}$").scale(.7)

+		vec3_text.shift(self.graph_origin+a3+0.2)

+		self.play(ShowCreation(vec3))

+		self.wait(.5)

+		self.play(ShowCreation(vec3_text))

+		self.wait(1)

+

+

+

+

+		

+

+

+

+

+

+

+

+

+

+

+

+		

+		

+	

+

+	

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Space_As_Functions.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Space_As_Functions.py
new file mode 100644
index 0000000..4f5614d
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Space_As_Functions.py
@@ -0,0 +1,62 @@
+from manimlib.imports import *

+from scipy import sin,cos

+class FunctionalVectorSpace(GraphScene):

+    CONFIG = {

+    "x_min": -5,

+    "x_max": 5,

+    "y_min": -5,

+    "y_max": 5,

+    "graph_origin": ORIGIN,

+    }

+    def construct(self):

+        self.setup_axes(animate = True)        

+        curve1 = self.get_graph(lambda x : sin(x), x_min=-5,x_max=5,color=YELLOW_E)

+        curve2 = self.get_graph(lambda x : cos(x), x_min=-5,x_max=5,color=RED)

+        self.play(ShowCreation(curve1))       

+        fx=TextMobject(r"$f(x)$",color=YELLOW_E).scale(0.7)

+        fx.shift(5*LEFT+0.7*UP)

+        self.play(ShowCreation(fx))

+        self.play(ShowCreation(curve2))

+        gx=TextMobject(r"$g(x)$",color=RED).scale(0.7)

+        gx.shift(5*LEFT+0.2*UP)

+        self.play(ShowCreation(gx))

+        self.wait(2)

+        scaling=TextMobject("Scaling f(x) by 2 units",color=GOLD).scale(0.65)

+        scaling.shift(3*LEFT+2.4*UP)

+        curve3 = self.get_graph(lambda x : 2*sin(x), x_min=-5,x_max=5,color=BLUE)

+        fx2=TextMobject(r"$2f(x)$",color=BLUE).scale(0.7)

+        fx2.shift(5*LEFT+1*UP)

+        self.play(Transform(curve1,curve3),FadeOut(fx),ShowCreation(fx2),ShowCreation(scaling))

+        self.wait(3)

+        hx = TextMobject(r"$h(x)$",color=PURPLE).scale(0.7)

+        hx.shift(4.9*LEFT+1.5*UP)

+        curve4 = self.get_graph(lambda x : 2*sin(x) + cos(x), x_min=-5,x_max=5,color=PURPLE)

+        self.play(ShowCreation(curve4),ShowCreation(hx))

+        self.play(FadeOut(curve2),FadeOut(curve1),FadeOut(fx2),FadeOut(gx),FadeOut(scaling))

+        hxn=TextMobject(r"$h(x)$",color=PURPLE).scale(0.7)

+        hxn.shift(3*RIGHT+2.4*UP)

+        equal = TextMobject("=").scale(0.7)

+        equal.shift(3.5*RIGHT+2.4*UP)

+        fx2n=TextMobject(r"$2f(x)$",color=BLUE).scale(0.7)

+        fx2n.shift(4.2*RIGHT+2.4*UP)

+        add=TextMobject("+").scale(0.7)

+        add.shift(4.8*RIGHT+2.4*UP)

+        gxn=TextMobject(r"$g(x)$",color=RED).scale(0.7)

+        gxn.shift(5.3*RIGHT+2.4*UP)

+        vector_add=TextMobject("Vector Addition",color=GOLD).scale(0.65)

+        vector_add.shift(3*UP+3*RIGHT)

+        self.play(ShowCreation(hxn),ShowCreation(equal),ShowCreation(fx2n),ShowCreation(add),ShowCreation(gxn),ShowCreation(vector_add))

+        self.wait(2)

+

+        

+

+

+

+

+

+

+     

+

+

+

+    
\ No newline at end of file