Encontrados 7 documentos, a visualizar página 1 de 1

Classes of non-Hermitian operators with real eigenvalues

Convexity of the Krein space tracial numerical range and Morse theory

In this paper we present a Krein space convexity theorem on the tracial-numerical range of a matrix. This theorem is the analogue of Westwick's theorem. The proof is an application of Morse theory.

Product of diagonal entries of the unitary orbit of a 3-by-3 normal matrix

Let N be a 3×3 normal matrix. We investigate the sets where U(3) is the group of 3×3 unitary matrices and 1[less-than-or-equals, slant]k[less-than-or-equals, slant]3. Geometric properties of these sets are studied, namely, star-shapedness and simple connectedness are investigated. A method for the numerical estimation of is also provided for normal matrices of size 3. ; http://www.sciencedirect.com/science/a...

The J-numerical range of a J-Hermitian matrix and related inequalities

Recently, indefinite versions of classical inequalities of Schur, Ky Fan and Rayleigh-Ritz on Hermitian matrices have been obtained for J-Hermitian matrices that are J-unitarily diagonalizable, J=Ir[circle plus operator](-Is),r,s>0. The inequalities were obtained in the context of the theory of numerical ranges of operators on indefinite inner product spaces. In this paper, the subject is revisited, relaxing th...

On the corners of certain determinantal ranges

Let A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of determinant one. Define [Delta](A)=det(AoQ):Q[set membership, variant]SO(n), where o denotes the Hadamard product of matrices. For a permutation [sigma] on 1,...,n, define It is shown that if the equation z[sigma]=det(AoQ) has in SO(n) only the obvious solutions (Q=([epsilon]i[delta][sigma]i,j), [epsilon]i=±1 such that [epsi...

The Elliptical and the Hyperbolical Range Theorems Revisited

International Conference on Engineering and Mathematics (ENMA'2007), July 9-11, 2007 - Bilbao, Spain. ; A geometrical proof of the Hyperbolical Range Theorem, concerning the numerical range of linear operators on 2-dimensional Krein spaces, is given. The classical Elliptical Range Theorem, which is the correspondent result for Hilbert spaces, is also obtained using the same technique. Both proofs depend on the...

The numerical range of 2-dimensional Krein spaces operators

The tracial numerical range of operators on a 2-dimensional Krein space is investigated. Results in the vein of those obtained in the context of Hilbert spaces are stated