On a theorem of Everitt, Thompson, and de Pillis
Miroslav Fiedler, Thomas L. Markham (1994)
Mathematica Slovaca
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Miroslav Fiedler, Thomas L. Markham (1994)
Mathematica Slovaca
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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.
Rufus Oldenburger (1940)
Compositio Mathematica
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Miroslav Fiedler, Vlastimil Pták (1962)
Czechoslovak Mathematical Journal
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Gerard Sierksma, Evert Jan Bakker (1986)
Compositio Mathematica
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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).