The matrix equation and related problems.
Al'pin, Yu.A., Ilyin, S.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Al'pin, Yu.A., Ilyin, S.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Branislav Martić (1984)
Publications de l'Institut Mathématique
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Mazanik, S.A. (1998)
Memoirs on Differential Equations and Mathematical Physics
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Larsen, Michael (1995)
The Electronic Journal of Combinatorics [electronic only]
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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).
João Lita da Silva, António Manuel Oliveira (2009)
Discussiones Mathematicae Probability and Statistics
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A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.
Janaki, T.M., Rangarajan, Govindan (2003)
International Journal of Mathematics and Mathematical Sciences
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Yurij Alekseevich Mitropol'ski, V. L. Kulik (1986)
Časopis pro pěstování matematiky
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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.