Congruence of Hermitian matrices by Hermitian matrices

• Tipo: Artigo em Revista Científica Internacional
• Data: 2007

Autores

Maria Isabel Bueno (Autor) Outra; Susana Borges Furtado (Autor) FEP; Charles Johnson (Autor) Outra

Revista

Título: Linear Algebra and Its Applications

Vol. 425

Páginas: 63-76

ISSN: 0024-3795

Editora: Elsevier

Indexação

ISI Web of Knowledge - 4 Citações

ISI Web of Science

Scopus - 6 Citações

Classificação Científica

FOS: Ciências exactas e naturais

Outras Informações

ID Authenticus: P-004-8K7

DOI: 10.1016/j.laa.2007.03.016

Abstract (EN): Two Hermitian matrices A, B E Mu (C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C is an element of M-n (C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible inertias of the Hermitian matrices C that carry the congruence. We also give necessary and sufficient conditions for any 2-by-2 nonsingular Hermitian matrices to be Hermitian-congruent. In both of the studied cases, we show that if A and B are real and Hermitian-congruent, then they are congruent by a real symmetric matrix. Finally we note that if A and B are 2-by-2 nonsingular real symmetric matrices having the same sign pattern, then there is always a real symmetric matrix C satisfying B = CAC. Moreover, if both matrices are positive, then C can be picked with arbitrary inertia.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 14