Hermitian-type generalized singular value decomposition with applications

SUMMARY For a pair of given Hermitian matrix A and rectangular matrix B with the same row number, we reformulate a well-known simultaneous Hermitian-type generalized singular value decomposition (HGSVD) with more precise structure and parameters and use it to derive some algebraic properties of the linear Hermitian matrix function A−BXB* and Hermitian solution of the matrix equation BXB* = A, and the canonical form of a partitioned Hermitian matrix and some optimization problems on its inertia and rank. Copyright © 2012 John Wiley & Sons, Ltd.