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: Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.1825
• Languages: English
• ISSNs: 1070-5325

Abstract

<abstract abstract-type="main" id="nla1825-abs-0001"> <title>SUMMARY</title> <p id="nla1825-para-0001">For a pair of given Hermitian matrix <italic>A</italic> and rectangular matrix <italic>B</italic> 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 <italic>A</italic>−<italic>BXB</italic>* and Hermitian solution of the matrix equation <italic>BXB</italic>* = <italic>A</italic>, and the canonical form of a partitioned Hermitian matrix and some optimization problems on its inertia and rank. Copyright © 2012 John Wiley &amp; Sons, Ltd.</p> </abstract>