Matrix correlation (Q1067717)

A correlation measure for an \(n\times p\) matrix X and an \(n\times q\) matrix Y assesses their relation without specifying either as a fixed target. This paper discusses a number of useful measures of correlation, with emphasis on measures which are invariant with respect to rotations or changes in singular values of either matrix. The maximization of matrix correlation with respect to transformations XL and YM is discussed where one or both transformations are constrained to be orthogonal. A factor analytic example is presented illustrating the advantages of various coefficients and varying the number of columns of the transformed matrices. (From authors' summary.)