Displaying similar documents to “On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix.”

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).