Inequalities for spreads of matrix sums and products.
Merikoski, Jorma K., Kumar, Ravinder (2004)
Applied Mathematics E-Notes [electronic only]
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Displaying similar documents to “A counterexample to Merikoski-Kumar conjecture on the product of normal matrices.”
Inequalities for spreads of matrix sums and products.
A. Horn's result on matrices with prescribed singular values and eigenvalues.
Tam, Tin-Yau (2010)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Interlacing inequalities for generalized singular values
María José Sodupe Zurbano (1986)
Extracta Mathematicae
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Simultaneous triangularization of commuting matrices for the solution of polynomial equations
Vanesa Cortés, Juan Peña, Tomas Sauer (2012)
Open Mathematics
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We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.
The Sherman-Morrison formula and eigenvalues of a special bordered matrix.
Trenkler, G., Trenkler, D. (2005)
Acta Mathematica Universitatis Comenianae. New Series
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On the determinantal inequalities.
Zhan, Shilin (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Central limit theorems for eigenvalues of deformations of Wigner matrices
M. Capitaine, C. Donati-Martin, D. Féral (2012)
Annales de l'I.H.P. Probabilités et statistiques
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In this paper, we study the fluctuations of the extreme eigenvalues of a spiked finite rank deformation of a Hermitian (resp. symmetric) Wigner matrix when these eigenvalues separate from the bulk. We exhibit quite general situations that will give rise to universality or non-universality of the fluctuations, according to the delocalization or localization of the eigenvectors of the perturbation. Dealing with the particular case of a spike with multiplicity one, we also establish a necessary...
A Brauer’s theorem and related results
Rafael Bru, Rafael Cantó, Ricardo Soto, Ana Urbano (2012)
Open Mathematics
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Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when...
A matrix inequality
Russell C. Thompson (1976)
Commentationes Mathematicae Universitatis Carolinae
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Inequalities on the singular values of an off-diagonal block of a Hermitian matrix.
Li, Chi-Kwong, Mathias, Roy (1999)
Journal of Inequalities and Applications [electronic only]
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A note on certain ergodicity coeflcients
Francesco Tudisco (2015)
Special Matrices
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We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector...