Repositório Colecção:
http://hdl.handle.net/10348/3630
2019-04-15T14:27:23ZSome further notes on the matrix equations ATXB+BTXTA = C and ATXB+BTXA =C
http://hdl.handle.net/10348/6723
Título: Some further notes on the matrix equations ATXB+BTXTA = C and ATXB+BTXA =C
Autor: Soares, Graça
Resumo: Dehghan and Hajarian, [4], investigated the matrix equations AT X B + BT XT A = C and AT X B + BT X A = C providing inequalities for the determinant of the solutions of these equations. In the same paper, the authors presented a lower bound for the product of the eigenvalues of the solutions to these matrix equations. Inspired by their work, we give some generalizations of Dehghan and Hajarian results. Using the theory of the numerical ranges, we present an inequality involving the trace of C when A,B,X are normal matrices satisfying AT B = BAT.2015-01-01T00:00:00ZInequalities for J-Hermitian matrices
http://hdl.handle.net/10348/5842
Título: Inequalities for J-Hermitian matrices
Autor: Soares, Graça; Bebiano, Natália; Nakazato, Hiroshi; Lemos, Rute; Providência, João
Resumo: Indefinite versions of classical results of Schur, Ky Fan and Rayleigh-Ritz on Hermitian matrices are stated to J-Hermitian matrices, J = Ir ⊕ −In − r, 0 < r < n). Spectral inequalities for the trace of the product of J-Hermitian matrices are presented. The inequalities are obtained in the context of the theory of numerical ranges of linear operators on indefinite inner product spaces.2005-01-01T00:00:00Z