Re: eigenvalue/eigenvector question again

From: Gordo (gordo20878_at_hotmail.com)
Date: 02/26/05 

Date: Sat, 26 Feb 2005 13:03:19 -0500

John wrote:
> I create a matrix using the following multiplication
> A = UDU'
> where U'U = I
> det U = 1
> now how do I recover U and D?
> Can U and D be exactly recovered at all?
> --j

You have left out a few pertinent details, but you are doing a coordinate
transformation to/from principal axes. In linear algebra, U usually denotes
an upper triangle, but not in this case. Your U is an orthogonal matrix
whose columns are the normalized eigenvectors of A (length=1). D is a
diagonal matrix of eigenvalues of A. The eigenvectors are the principal
axes; i.e., each column of U gives the direction cosines of a principal
axis. (I have given geometric interpretations in case you are in 2-D or
3-D.)

Gordon Everstine