On-Line Computer Graphics Notes

Inner Product Spaces

Overview

An inner product space is a linear (vector) space with a function that serves a purpose much like the dot product in two and three-dimensional space. With this inner product we can introduce the concept of orthogonality and orthogonal complements. It is also the case that an inner product space is a normed linear space and we can introduce the concept of orthonormal bases.

• The definition of an inner product space and the properties that these spaces satisfy including
  • The Schwartz Inequality
  • The Triangle Inequality
  • The Parallelogram Equation

• Orthogonality and Orthonormal Sets including
  • The Gram-Schmidt Orthogonalization Process

• Examples of Inner Product Spaces
  • The space of Continuous Functions on a closed interval

This document maintained by Ken Joy Comments to the Author All contents copyright (c) 1996, 1997 Computer Science Department, University of California, Davis All rights reserved.