Displaying similar documents to “Simultaneous triangularization of commuting matrices for the solution of polynomial equations”

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...

Condition numbers of Hessenberg companion matrices

Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)

Czechoslovak Mathematical Journal

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The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...

New bounds for the minimum eigenvalue ofM-matrices

Feng Wang, Deshu Sun (2016)

Open Mathematics

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Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.