Help for EIGENVEC

PURPOSE:
	EIGENVEC will compute the principal component transformation 
matrix for up to 32 input channels.  The covariance matrix, the transformation
matrix of eigen-vectors, and the eigen-values are printed.  This program
should normally be run via the procedure EIGEN.

OPERATION:

The measure of inter-dimensional correlation in the multi-variate
system is usually defined by the covariance matrix of the multi-variate
data.  The linear transformation that diagonalizes the covariance matrix 
can also be applied to the original data and produce a multi-variate 
system with an inter-dimensional correlation of zero, i.e.; completely
uncorrelated multi-variate data.  The linear transformation that
accomplishes this is the matrix of eigen-vectors or characteristic vectors.

A common application of this transformation is to reduce the 
dimensionality of a multi-variate system.  The objective is to summarize
most of the variance, or information content, in a system with a 
lessor number of 'artificial' variates, i.e.; principal components. 
Effectively, by uncorrelating the system, we are compressing most of the
information into a system with lower dimensionality. 

Assume an n-variate system ( n channels of data ).  Let K be the 
n x n covariance matrix of this data and A be the matrix of eigen-vectors
of K.  Associated with each eigen-vector A(j) there is an eigen-value or 
characteristic root, e(j).

	Let A(j) = (a(1j),a(2j),...,a(nj)) be the eigen-vector corresponding 
	to the jth largest eigen-value.

	Let X = (x(1),x(2),...,x(n)) be the n-variate observation 
	( n-dimensional pixel ).

	Then the jth principle component is: v(j) = A(j)  X = a(ij)x(i)

NOTE:  The jth eigen-value is actually the variance in the jth 
principle componemt dimension.  Therefore, the eigen-values are useful 
as a measure the information content that can be expected in the output 
pictures.
WRITTEN BY:  J. D. Addington,   19 Oct. 1979

CURRENT COGNIZANT PROGRAMMER:  Ron Alley
Made portable for UNIX         W. Huey (CRI) 1994
Removed aliases and lets from tst pdf.  FR76949  May 1995