Eventually DSDD Matrices and Eigenvalue Localization
نویسندگان
چکیده
منابع مشابه
Ela an Eigenvalue Inequality and Spectrum Localization for Complex Matrices∗
Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...
متن کاملAn eigenvalue inequality and spectrum localization for complex matrices
Using the notions of the numerical range, Schur complement and unitary equivalence, an eigenvalue inequality is obtained for a general complex matrix, giving rise to a region in the complex plane that contains its spectrum. This region is determined by a curve, generalizing and improving classical eigenvalue bounds obtained by the Hermitian and skew-Hermitian parts, as well as the numerical ran...
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A matrix A ∈ Rn×n is eventually nonnegative (respectively, eventually positive) if there exists a positive integer k0 such that for all k ≥ k0, A ≥ 0 (respectively, A > 0). Here inequalities are entrywise and all matrices are real and square. An eigenvalue of A is dominant if its magnitude is equal to the spectral radius of A. A matrix A has the strong Perron-Frobenius property if A has a uniqu...
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In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کامل“odd” Matrices and Eigenvalue Accuracy
A definition of even and odd matrices is given, and some of their elementary properties stated. The basic result is that if λ is an eigenvalue of an odd matrix, then so is −λ. Starting from this, there is a consideration of some ways of using odd matrices to test the order of accuracy of eigenvalue routines. 1. Definitions and some elementary properties Let us call a matrix W even if its elemen...
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ژورنال
عنوان ژورنال: Symmetry
سال: 2018
ISSN: 2073-8994
DOI: 10.3390/sym10100448