14 lines
416 B
Markdown
14 lines
416 B
Markdown
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---
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title: Inner Product Spaces
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---
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## Inner Product Spaces
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### Introduction
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Let V be a vector space over field F. An inner product is a function that assigns to every ordered pair of vector x and y in V, a scalar in F, denoted by <x,y> such that for all x,y in V and a in F these hold:
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* <x+z,y>=<x,y>+<x,z>
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* <ax,y>=a<x,y>
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* <X,Y>=<y,x> (X and Y denote conjugate of x and y respectively)
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* <x,x>=0 for all x!=0
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