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diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py
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index 0000000..97b9696
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py
@@ -0,0 +1,182 @@
+from manimlib.imports import *

+from scipy import sin,cos

+class Inner_Product_Space_Example(GraphScene):

+    CONFIG = {

+        "x_min" : 0,

+        "x_max" : 5,

+        "y_min" : 0,

+        "y_max" : 6,

+        "y_tick_frequency" : 1, 

+        "x_tick_frequency" : 1, 

+        "axes_color":LIGHT_GRAY,

+        "x_labeled_nums" : list(range(6)),

+        "y_labeled_nums" : list(range(6))

+    }   

+    def construct(self):

+        self.setup_axes(animate=True)

+        text = TextMobject(r"$f(x), g(x), h(x) \in C[0, 2]$",color=GOLD).scale(0.5).shift(3.5*UP+5.5*LEFT)

+        fx = TextMobject(r"$f(x)$ = sin(x)",color=GOLD).scale(0.5).shift(3*UP+6*LEFT)

+        gx = TextMobject(r"$g(x)$ = x",color=GOLD).scale(0.5).shift(2.5*UP+6.25*LEFT)

+        hx = TextMobject(r"$h(x)$ = 1.4",color=GOLD).scale(0.5).shift(2*UP+6.2*LEFT)

+

+        curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2,color=RED)

+        curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2,color=DARK_BLUE)

+        curve3 = self.get_graph(lambda x : 1.4, x_min=0,x_max=2,color=GREEN)

+        text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.7*DOWN)

+        

+        text2 = TextMobject(r"$g(x)$").scale(0.5).shift(0.34*DOWN)

+        text3 = TextMobject(r"$h(x)$").scale(0.5).shift(1.1*DOWN)

+

+        

+        self.play(ShowCreation(text))

+        self.play(ShowCreation(curve1),ShowCreation(text1),ShowCreation(fx))

+        self.wait(1)

+        self.play(ShowCreation(curve2),ShowCreation(text2),ShowCreation(gx))

+        self.wait(1)

+        self.play(ShowCreation(curve3),ShowCreation(text3),ShowCreation(hx))

+        self.wait(2)

+        curve4 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2,color=YELLOW)

+        text4 = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(0.5*UP+0.5*RIGHT)

+        self.wait(1.5)

+

+        self.play(ShowCreation(curve4),ShowCreation(text4),FadeOut(curve2),FadeOut(text2),FadeOut(curve1),FadeOut(text1))

+        self.wait(1.5)

+        text5 = TextMobject(r"\text{$<f(x) + g(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (f(x) + g(x))h(x)$ $dx$}",r"\text{= 4.78}").scale(0.57).shift(3.3*RIGHT+3.5*UP)

+        text5[1].set_color(ORANGE)

+        self.play(ShowCreation(text5))

+

+        curve5 = self.get_graph(lambda x : (sin(x) + x)*1.6, x_min=0,x_max=2,color=ORANGE)

+        text6 = TextMobject(r"$(f(x) + g(x))\cdot h(x)$").scale(0.5).shift(2.2*UP+0.72*RIGHT)

+        area1 = self.get_area(curve5,0,2)

+        area1.set_color(ORANGE)

+        self.wait(1)

+        self.play(FadeOut(curve4),FadeOut(text4),FadeOut(curve3),FadeOut(text3),ShowCreation(curve5),ShowCreation(text6),ShowCreation(area1))

+        self.wait(2)

+        text7 = TextMobject(r"\text{$<f(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (f(x)h(x)$ $dx$}",r"\text{= 1.98}").scale(0.57).shift(4.5*RIGHT+3*UP)

+        text7[1].set_color(BLUE)

+        self.play(ShowCreation(text7))

+        self.wait(1.5)

+        curve6 = self.get_graph(lambda x : (sin(x))*1.6, x_min=0,x_max=2,color=BLUE)

+        text8 = TextMobject(r"$f(x)\cdot h(x)$").scale(0.5).shift(0.9*DOWN+0.3*RIGHT)

+        area2 = self.get_area(curve6,0,2)

+        self.play(ShowCreation(curve6),ShowCreation(text8),ShowCreation(area2))

+        self.wait(1.5)

+        text9 = TextMobject(r"\text{$<g(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (g(x)h(x)$ $dx$}",r"\text{= 2.8}").scale(0.57).shift(4.5*RIGHT+2.5*UP)

+        text9[1].set_color(MAROON_B)

+        self.play(ShowCreation(text9))

+        self.wait(1.5)

+        curve7 = self.get_graph(lambda x : x*1.6, x_min=0,x_max=2,color=MAROON_B)

+        text10 = TextMobject(r"$g(x)\cdot h(x)$").scale(0.5).shift(0.3*RIGHT+0.78*UP)

+        area3 = self.get_area(curve7,0,2)

+        area3.set_color(MAROON_B)

+        self.play(ShowCreation(curve7),ShowCreation(text10),ShowCreation(area3))

+        self.wait(2.6)

+        curve8 = self.get_graph(lambda x : (sin(x))*1.6 + x*1.6, x_min=0,x_max=2,color=RED_C)

+        area4 = self.get_area(curve8,0,2)

+        area4.set_color(RED_C)

+        text11 = TextMobject(r"$f(x)h(x) + g(x)h(x)$").scale(0.5).shift(2.2*UP + 0.76*RIGHT)

+        self.play(FadeOut(curve6),FadeOut(text8),FadeOut(curve7),FadeOut(text10),FadeOut(area2),FadeOut(area3),ShowCreation(curve8),ShowCreation(area4))

+        self.wait(1)

+        self.play(Transform(text6,text11))

+        self.wait(1.7)

+        text12 = TextMobject(r"$<f(x) + g(x), h(x)>$ = $<f(x), h(x)>$ + $<g(x), h(x)>$").scale(0.465).shift(0.7*UP+4*RIGHT)

+        rect1 = Rectangle(height=0.5)

+        rect1.surround(text12)

+        self.play(ShowCreation(text12),ShowCreation(rect1))

+        self.wait(3)

+        self.play(FadeOut(text6),FadeOut(text5),FadeOut(text7),FadeOut(text9),FadeOut(text12),FadeOut(rect1),FadeOut(curve8),FadeOut(area4),FadeOut(text11),FadeOut(curve5),FadeOut(area1))

+

+        curve2.set_color(ORANGE)

+        self.play(ShowCreation(curve1),ShowCreation(text1))

+        self.wait(1)

+        self.play(ShowCreation(curve2),ShowCreation(text2))

+        self.wait(2)

+        curve9 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2,color=GREEN)

+        text13 = TextMobject(r"$2f(x)$").scale(0.5).shift(0.75*DOWN)

+        self.play(Transform(curve1,curve9),Transform(text1,text13))

+        self.wait(1.5)

+

+        text14 = TextMobject(r"\text{$<2f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} (2f(x))g(x)$ $dx$}",r"\text{= 3.48}").scale(0.57).shift(4*RIGHT+3.5*UP)

+        text14[1].set_color(YELLOW)

+        self.play(ShowCreation(text14))

+        self.wait(2.2)

+        curve10 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2,color=YELLOW)

+        text15 = TextMobject(r"$2f(x)\cdot g(x)$").scale(0.5).shift(0.35*RIGHT+1.03*UP)

+        area5 = self.get_area(curve10,0,2)

+        area5.set_color(YELLOW)

+        self.play(ShowCreation(area5),ShowCreation(curve10),ShowCreation(text15),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))

+        self.wait(2)

+        text16 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 1.74}").scale(0.57).shift(3.8*RIGHT+2.9*UP)

+        text16[1].set_color(TEAL)

+        self.play(ShowCreation(text16))

+        self.wait(1.7)

+        curve11 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=TEAL)

+        area6 = self.get_area(curve11,0,2)

+        area6.set_color(TEAL)

+        text17 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.4*RIGHT+0.7*DOWN)

+        self.play(ShowCreation(curve11),ShowCreation(text17),ShowCreation(area6))

+        self.wait(2)

+

+        text18 = TextMobject(r"\text{$2 <f(x), g(x)>$ = ",r"\text{$2 \int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 3.48}").scale(0.57).shift(4*RIGHT+2.3*UP)

+        text18[1].set_color(DARK_BLUE)

+        self.play(ShowCreation(text18))

+        self.wait(2)

+        curve12 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2,color=DARK_BLUE)

+        area7 = self.get_area(curve12,0,2)

+        area7.set_color(DARK_BLUE)

+        text19 = TextMobject(r"= $2( f(x)\cdot g(x) )$").scale(0.5).shift(1.89*RIGHT+1.03*UP)

+        self.play(ShowCreation(curve12),ShowCreation(area7),ShowCreation(text19),FadeOut(text17),FadeOut(area6),FadeOut(curve11))

+

+        self.wait(2.5)

+        text20 = TextMobject(r"$<2f(x), g(x)>$ = $2<f(x), g(x)>$").scale(0.57).shift(0.6*DOWN+4*RIGHT)

+        rect2 = Rectangle(height=0.5)

+        rect2.surround(text20)

+        self.play(ShowCreation(text20),ShowCreation(rect2))

+        self.wait(3)

+

+        self.play(FadeOut(text14),FadeOut(text15),FadeOut(text19),FadeOut(text16),FadeOut(text18),FadeOut(rect2),FadeOut(curve10),FadeOut(area5),FadeOut(curve12),FadeOut(area7),FadeOut(text20))

+        curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2,color=YELLOW)

+        text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.77*DOWN)

+        self.play(ShowCreation(curve1),ShowCreation(text1))

+        self.wait(1.5)

+        self.play(ShowCreation(curve2),ShowCreation(text2))

+        self.wait(1.7)

+        text21 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 1.74}").scale(0.57).shift(3.5*RIGHT+3*UP)

+        text21[1].set_color(GREEN)

+        self.play(ShowCreation(text21))

+        self.wait(2)

+        curve13 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=GREEN)

+        area8 = self.get_area(curve13,0,2)

+        area8.set_color(GREEN)

+        text22 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.32*RIGHT+0.7*DOWN)

+        self.play(ShowCreation(curve13),ShowCreation(area8),ShowCreation(text22),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))

+        self.wait(2.2)

+        curve14 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=RED)

+        area9 = self.get_area(curve14,0,2)

+        area9.set_color(RED)

+        self.play(ShowCreation(curve14),ShowCreation(area9))

+        text23 = TextMobject(r"= $\overline{f(x)\cdot g(x)}$").scale(0.5).shift(0.7*DOWN+1.7*RIGHT)

+        self.play(ShowCreation(text23))

+        self.wait(2)

+        text24 = TextMobject(r"For all the real functions").scale(0.5).shift(2*RIGHT+2*UP)

+        text25 = TextMobject(r"$<\overline{f(x), g(x)}>$ = $<f(x), g(x)>$").scale(0.5).shift(2*RIGHT+1.4*UP)

+        rect3 = Rectangle(height=0.7)

+        rect3.surround(text25)

+        self.play(ShowCreation(text24),ShowCreation(text25),ShowCreation(rect3))

+        self.wait(3)

+

+        

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