Fermat's equation for matrices or quaternions over q-adic fields
Paulo Ribenboim (2004)
Acta Arithmetica
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Paulo Ribenboim (2004)
Acta Arithmetica
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Fallat, Shaun M., Johnson, Charles R., Smith, Ronald L. (2000)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Johnson, Charles R., Kroschel, Brenda K. (1996)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Zhu, Yan, Zhang, Cheng-Yi, Liu, Jun (2011)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Li, Aihua, Randall, Duane (2002)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Copi, Irving M., Harary, Frank (1953)
Portugaliae mathematica
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Bidard, Christian (2007)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Robert Costa, Patrick Dynes, Clayton Petsche (2016)
Acta Arithmetica
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We prove that if an n×n matrix defined over ℚ ₚ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ℚ ₚ, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a p-adic analogue of the Perron-Frobenius theorem for positive real matrices.
Irina Karelin, Leonid Lerer (2001)
International Journal of Applied Mathematics and Computer Science
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It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...
Lee, Gwang-Yeon, Shader, Bryan L. (1998)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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D. Brink, H. Godinho, P. H. A. Rodrigues (2008)
Acta Arithmetica
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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.
Janaki, T.M., Rangarajan, Govindan (2003)
International Journal of Mathematics and Mathematical Sciences
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