Alternative characterizations of the extended Wedderburn-Guttman theorem (Q875020)

The authors give alternative characterization of the extended Wedderburn-Guttman theorem using the product singular value decomposition (PSVD) of matrix triplets. Transforming the matrices into quasi-diagonal form has proven to be useful in establishing many matrix results in a variety of statistical contexts. PSVD of matrix triplets was initially developed as a way of obtaining the ordinary SVD of a product of the matrix triplets without actually computing the product. Although PSVD was originally developed for computational purposes, this paper demonstrates that it is also useful as a tool for a mathematical proof.