On the nonuniqueness of the factorization factors in the product singular value decomposition
The product singular value decomposition, as is used in e.g. the Procrustes problem, is described in a partitioned form such that 5 arbitrary orthogonal blocks, 3 arbitrary rectangular blocks and one arbitrary nonsingular block determine the choices available when the decomposition is not unique. The sizes of the blocks is determined by ranks of the matrices and their product, and the multiplicity of the singular values.
scientific article; zbMATH DE number 1506625
scientific article