Canonical Correlation

Suppose is an matrix and is an matrix. The cosine of the angle between two linear combinations and is Consider the problem of finding the maximum, the minimum, and possible other stationary values of .

are two matrices of dimensions, respectiSpecifically there exists a non-singular of order and a non-singular of order such that Here and are diagonal, with the and leading diagonal elements equal to one and all other elements zero. is a matrix with the non-zero canonical correlations in non-increasing order along the diagonal and zeroes everywhere else.

http://en.wikipedia.org/wiki/Principal_angles http://meyer.math.ncsu.edu/Meyer/PS_Files/AnglesBetweenCompSubspaces.pdf