Merge pull request #3 from FOSSEE/master

Added others' files

13 files changed, 420 insertions, 0 deletions

diff --git a/FSF-2020/linear-algebra/vector-spaces/README.md b/FSF-2020/linear-algebra/vector-spaces/README.md
index e69de29..03f6a03 100644
--- a/FSF-2020/linear-algebra/vector-spaces/README.md
+++ b/FSF-2020/linear-algebra/vector-spaces/README.md
@@ -0,0 +1,9 @@
+# Contributer: Simran Chhattani

+My Github Account : <a href="https://github.com/simranchhattani">simranchhattani</a>

+<br/></br>

+## Sub-Topics Covered:

++ Vector Spaces

++ Basis of a Vector Space and Subspace

++ Polynomial and Function Vector Space

++ Inner Product Spaces

++ Dual of a Vector Space

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Straight_Line_through_Origin.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Straight_Line_through_Origin.py
new file mode 100644
index 0000000..5790d2e
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Straight_Line_through_Origin.py
@@ -0,0 +1,48 @@
+from manimlib.imports import *

+from scipy import exp, sin, log,tan,cos

+class Straight_Line(GraphScene):

+    CONFIG = {

+        "x_min" : -4,

+        "x_max" : 4,

+        "y_min" : -4,

+        "y_max" : 4,

+        "y_tick_frequency" : 1, 

+        "x_tick_frequency" : 1, 

+        "x_labeled_nums" : list(np.arange(-4,5,1)),

+        "y_labeled_nums" : list(np.arange(-4,5,1)),

+        "graph_origin" : ORIGIN+0.7*DOWN,

+        "axes_color" : GREY,

+        "x_axis_width": 6,

+        "y_axis_height":6,

+    }   

+    def construct(self):

+        self.setup_axes(animate=True)

+        line_1 = self.get_graph(lambda x : x, x_min=-3,x_max=3,color=YELLOW)

+        self.play(ShowCreation(line_1))

+        text1 = TextMobject("ax + by = 0",color=BLUE_B)

+        text1.shift(3*RIGHT+2*UP)

+        text1.scale(0.65)

+        dot = Dot(color=BLUE_B).shift(0.7*DOWN)

+        dot.scale(1.3)

+        self.play(ShowCreation(dot))

+        text2 = TextMobject("Line passing through the origin")

+        text2.scale(0.7)

+        text2.shift(3.5*UP)

+        self.play(ShowCreation(text1),ShowCreation(text2))

+        self.wait(1)

+        self.play(FadeOut(line_1),FadeOut(text2),FadeOut(text1))

+        text4=TextMobject("Line not passing through the origin")

+        text4.scale(0.7)

+        text4.shift(3.5*UP)

+        self.play(ShowCreation(text4))

+        

+        line_2 = self.get_graph(lambda x : 2.5*x +1, x_min = -2, x_max=1, color = RED)

+        text3 = TextMobject(r"ax + by $\neq 0$",color=BLUE_B)

+        text3.scale(0.65)

+        self.play(ShowCreation(line_2))

+        text3.shift(1.5*RIGHT+2.2*UP)

+        self.play(ShowCreation(text3))

+        self.wait(1)

+        

+    

+        
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
new file mode 100644
index 0000000..ada173e
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
@@ -0,0 +1,82 @@
+from manimlib.imports import *

+class Subspace_Example(Scene):

+    def construct(self):

+        sq = Square(side = 2, color=BLACK).shift(2*LEFT)

+        sq.set_fill(color=RED,opacity=350)

+        line1=Line(color=BLACK).shift(2*LEFT)

+        line1.rotate(np.pi/2)

+        line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)

+        line2.scale(0.5)

+        line3=Line(color=BLACK).shift(+1.5*LEFT)

+        line3.scale(0.5)

+        a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)

+        a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)

+        a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)

+        a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)

+        big_rect=Rectangle().scale(3).shift(0.5*DOWN)

+        big_rect.set_fill(color=GREY,opacity=350)

+        vec_space=TextMobject("$Vector Space$").scale(0.77).shift(4.5*RIGHT+3.5*UP)

+        sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.77).shift(3.8*RIGHT+2*UP)

+        self.play(ShowCreation(vec_space))

+        self.play(ShowCreation(big_rect),ShowCreation(sub))

+        self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))

+        rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)

+        rec.rotate(np.pi/2)

+        rec.set_fill(color=BLUE,opacity=350)

+        line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)

+        line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)

+        line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)

+        b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)

+        b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)

+        b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)

+        b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)

+        self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))

+        self.wait(1)

+        text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)

+        text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)

+        self.play(ShowCreation(text1),ShowCreation(text2))

+        self.wait(3)

+        self.play(FadeOut(text1),FadeOut(text2))

+        rec.shift(3*LEFT+2.01*DOWN)

+        line4.shift(3*LEFT+2*DOWN)

+        line5.shift(3*LEFT+2*DOWN)

+        line6.shift(3*LEFT+2*DOWN)

+        b1.shift(3.1*LEFT+2.1*DOWN)

+        b2.shift(3.1*LEFT+2.1*DOWN)

+        b3.shift(2.9*LEFT+2*DOWN)

+        b4.shift(2.9*LEFT+2.3*DOWN)

+        self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))

+        self.wait(2)

+        

+        text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)

+        text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)

+        text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)

+        self.play(ShowCreation(text3),ShowCreation(text4))

+        self.wait(3)

+        rec.set_fill(color=GREY,opacity=350)

+        self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))

+        sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)

+        sq1.set_fill(color=RED,opacity=350)

+        sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)

+        sq2.set_fill(color=RED,opacity=350)

+        rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)

+        rec1.set_fill(color=RED,opacity=350)

+        rec2=Rectangle(height=1.5,width=1,color=BLACK)

+        rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)

+        self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))

+        a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)

+        b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)

+        c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)

+        d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)

+        self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))

+        self.wait(2.3)

+        text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)

+        text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)

+        text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)

+        self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))

+        self.wait(3)

+

+        

+

+

+

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Unit_Circle.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Unit_Circle.py
new file mode 100644
index 0000000..2973f08
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Unit_Circle.py
@@ -0,0 +1,68 @@
+from manimlib.imports import *

+import numpy as np

+import math

+

+class Unit_Circle(GraphScene):

+    CONFIG = {

+        "x_min" : -3,

+        "x_max" : 3,

+        "y_min" : -3,

+        "y_max" : 3,

+        "y_tick_frequency" : 1, 

+        "x_tick_frequency" : 1, 

+        "x_labeled_nums" : list(np.arange(-3,4,1)),

+        "y_labeled_nums" : list(np.arange(-3,4,1)),

+        "graph_origin" : ORIGIN,

+        "axes_color" : GREY,

+        "x_axis_width": 6,

+        "y_axis_height":6,

+    }   

+

+    def construct(self):

+        self.setup_axes(animate = True)

+        circle = Circle(radius=1,color=BLUE)

+        self.play(ShowCreation(circle))

+        dot1 = Dot(color=RED).scale(0.7)

+        dot1.shift(1*UP)

+        dot2 = Dot(color=RED).scale(0.7)

+        dot2.shift(1*LEFT)

+        dot3 = Dot(color=RED).scale(0.7)

+        dot3.shift(1*DOWN)

+        dot4 = Dot(color=RED).scale(0.7)

+        dot4.shift(1*RIGHT)

+        dot5= Dot(color=RED).scale(0.7)

+        dot6 = Dot(color=RED).scale(0.7)

+        dot5.shift(0.5*RIGHT+(math.sqrt(3)/2)*UP)

+        dot6.shift(0.5*LEFT+(math.sqrt(3)/2)*DOWN)

+        dot7 = Dot(color=RED).scale(0.7)

+        dot7.shift(math.sqrt(2)/2*RIGHT+math.sqrt(2)/2*UP)

+        dot8 = Dot(color=RED).scale(0.7)

+        dot8.shift(math.sqrt(2)/2*LEFT+math.sqrt(2)/2*UP)

+        dot9 = Dot(color=RED).scale(0.7)

+        dot9.shift(0.5*LEFT+(math.sqrt(3)/2)*UP)

+        dot10 = Dot(color=RED).scale(0.7)

+        dot10.shift(math.sqrt(3)/2*LEFT+0.5*UP)

+        dot11=Dot(color=RED).scale(0.7)

+        dot11.shift(math.sqrt(3)/2*RIGHT+0.5*UP)

+        dot12= Dot(color=RED).scale(0.7)

+        dot12.shift(math.sqrt(3)/2*LEFT+0.5*DOWN)

+        dot13=Dot(color=RED).scale(0.7)

+        dot13.shift(math.sqrt(2)/2*RIGHT+math.sqrt(2)/2*DOWN)

+        dot14=Dot(color=RED).scale(0.7)

+        dot14.shift(math.sqrt(2)/2*LEFT+math.sqrt(2)/2*DOWN)

+        dot15=Dot(color=RED).scale(0.7)

+        dot15.shift(math.sqrt(3)/2*RIGHT+0.5*DOWN)

+        dot16=Dot(color=RED).scale(0.7)

+        dot16.shift(0.5*RIGHT+(math.sqrt(3)/2)*DOWN)

+        self.play(ShowCreation(dot1),ShowCreation(dot2))

+        self.play(ShowCreation(dot3),ShowCreation(dot4))

+        self.play(ShowCreation(dot5),ShowCreation(dot6))

+        self.play(ShowCreation(dot7),ShowCreation(dot8))

+        self.play(ShowCreation(dot9),ShowCreation(dot10))

+        self.play(ShowCreation(dot11),ShowCreation(dot12))

+        self.play(ShowCreation(dot13),ShowCreation(dot14))

+        self.play(ShowCreation(dot15),ShowCreation(dot16))

+        self.wait(4)

+    

+

+

diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Straight_Line_Through_Origin.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Straight_Line_Through_Origin.gif
new file mode 100644
index 0000000..b7695a4
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Straight_Line_Through_Origin.gif
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
new file mode 100644
index 0000000..32b02be
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Unit_Circle.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Unit_Circle.gif
new file mode 100644
index 0000000..165d040
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Unit_Circle.gif
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
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/3D_Vector_Space.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/3D_Vector_Space.gif
new file mode 100644
index 0000000..137546a
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/3D_Vector_Space.gif
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Function_Vector_Space_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Function_Vector_Space_Example.gif
new file mode 100644
index 0000000..d9edf46
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Function_Vector_Space_Example.gif
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif
new file mode 100644
index 0000000..ed65f8a
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif