home | section main page


inner product space

Table of Contents

1. Introduction

An inner product space is a normed vector space with an inner product defined. This inner product obeys the following properties:

(1)x,y=y,x(2)ax+by,z=ax,z+by,z(3)x,x>0,x>0(4)x,x=0,x=0

where y,x is the complex conjugate of x,y. This gives rise to a normed vector space:

(5)x=x,x
Copyright © 2024 Preston Pan