Encontrados 11 documentos, a visualizar página 1 de 2
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...
Flat portions on the boundary of the indefinite numerical range of 3×3 matrices
Bebiano, N.; Providência, J. da; Teixeira, R.We focus on complex 3×3 matrices whose indefinite numerical ranges have a flat portion on the boundary. The results here obtained are parallel to those of Keeler, Rodman and Spitkovsky for the classical numerical range. ; http://www.sciencedirect.com/science/article/B6V0R-4S09585-1/1/cfd4cc3f5f7e4af2bc2e55b75b3a397b
Geometry of the numerical range of Krein space operators
Bebiano, N.; Providência, J. da; Teixeira, R.The characteristic polynomial of the pencil generated by two J-Hermitian matrices is studied in connection with the numerical range. Geometric properties of the numerical range of linear operators on an inde nite inner product space are investigated. The point equation of the associated curve of the numerical range is derived, following Fiedler's approach for de nite inner product spaces. The classi cation of ...
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...
Inequalities for quantum relative entropy
Bebiano, N.; Lemos, R.; Providência, J. daSome logarithmic trace inequalities involving the notions of relative entropy are reobtained from a log-majorization result. The thermodynamic inequality is generalized and a chain of equivalent statements involving this inequality and the Peierls-Bogoliubov inequality is obtained. ; http://www.sciencedirect.com/science/article/B6V0R-4CPM5VG-2/1/d98926b2da1f2e0c291953700e9a24db
Three observations on the determinantal range
Bebiano, N.; Soares, G.Let A, C [set membership, variant] Mn, the algebra of n × n complex matrices. The set of complex numbersis the C-determinantal range of A. In this note, it is proved that [Delta]C(A) is an elliptical disc for A, C [set membership, variant] M2. A necessary and sufficient condition for [Delta]C(A) to be a line segment is given when A and C are normal matrices with pairwise distinct eigenvalues. The linear operato...
On the geometry of numerical ranges in spaces with an indefinite inner product
Bebiano, N.; Lemos, R.; Providência, J. da; Soares, G.Geometric properties of the numerical ranges of operators on an indefinite inner product space are investigated. In particular, classes of matrices are presented such that the boundary generating curves of the J-numerical range are hyperbolical. The curvature of the J-numerical range at a boundary point is studied, generalizing results of Fiedler on the classical numerical range. ; http://www.sciencedirect.c...
Numerical ranges of unbounded operators arising in quantum physics
Bebiano, N.; Lemos, R.; Providência, J. daCreation and annihilation operators are used in quantum physics as the building blocks of linear operators acting on Hilbert spaces of many body systems. In quantum physics, pairing operators are defined in terms of those operators. In this paper, spectral properties of pairing operators are studied. The numerical ranges of pairing operators are investigated. In the context of matrix theory, the results give th...
Matrix inequalities in Statistical Mechanics
Bebiano, N.; Providência Jr., J. da; Lemos, R.Some matrix inequalities used in statistical mechanics are presented. A straightforward proof of the Thermodynamic Inequality is given and its equivalence to the Peierls–Bogoliubov inequality is shown.
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