Cover matrices of posets and their spectra

Milica Anđelić; C. M. da Fonseca

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Simultaneous triangularization of commuting matrices for the solution of polynomial equations

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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.

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Trenkler, G., Trenkler, D. (2005)

Acta Mathematica Universitatis Comenianae. New Series

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Grone, Robert, Merris, Russell (1988)

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A note on certain ergodicity coeflcients

Francesco Tudisco (2015)

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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...

A sparsity result on nonnegative real matrices with given spectrum

Thomas Laffey (1997)

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Let σ=(λ1,...,λn) be the spectrum of a nonnegative real n × n matrix. It is shown that σ is the spectrum of a nonnegative real n × n matrix having at most ${(n + 1)}^{2} / 2 - 1$ nonzero entries.

Existence of matrices with prescribed entries.

Ion Zaballa (1986)

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