Fancy Inner Products

Linear Methods of Applied Mathematics

Evans M. Harrell II and James V. Herod*

#### *(c) Copyright 1994-1997 by Evans M. Harrell
II and James V. Herod. All rights reserved.

**
Examples II.2, continued.
**

**
4. Other inner products for functions. We can generalize
Example 3 in various ways. The first is to insert a
positive weight function w(x): **

Another is to make the functions and integrals multidimensional, running over
some region
:

**
5. An inner product for matrices considered as vectors.
Let the vector space V be the set of mxn matrices. Define the
***adjoint* M* of a matrix M with entries m_{jk} to be the nxm matrix the
entries of which are
Define the trace of a matrix by
(sum the diagonal elements). Then

**
<M,N> := Tr(M N*) is an inner
product.
**

**
**

**
Or - here is a really great one - we could have weight functions and lots of
dimensions! Yeah.....**

**
**

**
Link to
**

**
chapter II**

Table of Contents

Evans Harrell's home page
Jim Herod's home page
**
**