Displaying similar documents to “Bounds for the singular values of a matrix involving its sparsity pattern.”

Z -pencils.

McDonald, Judith J., Olesky, D.Dale, Schneider, Hans, Tsatsomeros, Michael J., van den Driessche, P. (1998)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

Jianxing Zhao, Caili Sang (2016)

Open Mathematics

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Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.

The problem of kings.

Larsen, Michael (1995)

The Electronic Journal of Combinatorics [electronic only]

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On a nonnegative irreducible matrix that is similar to a positive matrix

Raphael Loewy (2012)

Open Mathematics

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Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.

Sufficient conditions to be exceptional

Charles R. Johnson, Robert B. Reams (2016)

Special Matrices

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A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).