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On the Courant-Fischer theory for Krein spaces
Bebiano, N.; Nakazato, H.; Providência, J. dahttp://www.sciencedirect.com/science/article/B6V0R-4V462G8-2/2/25c16be9e99d2fbaa89b7c1a6a47e95f
The boundary of the Krein space tracial numerical range, an algebraic approach ...
Bebiano, N.; Nakazato, H.; Nata, A.; Providência, J. daIn this article, tracial numerical ranges associated with matrices in an inde nite inner product space are investigated. The boundary equations of these sets are obtained and the case of the boundary being a polygon is studied. As an application, a numerical algorithm for plotting the tracial numerical range of an arbitrary complex matrix, is presented. Our approach uses the elementary idea that the boundary ma...
Inequalities for J-Hermitian matrices
Bebiano, N.; Nakazato, H.; Providência, J. da; Lemos, R.; Soares, G.Indefinite versions of classical results of Schur, Ky Fan and Rayleigh-Ritz on Hermitian matrices are stated to J-Hermitian matrices, J = Ir [circle plus operator] -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 sp...
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