Hermitian‐type generalized singular value decomposition with applications. Issue 1 (17th January 2012)

• Record Type: Journal Article
• Authors: Liu, Yonghui; Tian, Yongge
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 1(2013:Jan.)
• Page Start: 60
• Page End: 73
• Publication Date: 2012-01-17
• Subjects: Hermitian‐type generalized singular value decomposition -- matrix function -- matrix equation -- Hermitian‐type partitioned matrix -- rank and inertia optimization; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.1825
• Languages: English
• ISSNs: 1070-5325

Abstract

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.