A rational canonical form for matrix fields
J. Beard (1974)
Acta Arithmetica
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J. Beard (1974)
Acta Arithmetica
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Thompson, R.C. (1962)
Portugaliae mathematica
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Cain, Bryan E., Zaballa, Ion (1992)
Portugaliae mathematica
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H. S. Thurston (1939)
Compositio Mathematica
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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.
Acosta-de-Orozco, Maria T., Gomez-Calderon, Javier (1992)
International Journal of Mathematics and Mathematical Sciences
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Xiaonan Hu, Charles R. Johnson, Caroline E. Davis, Yimeng Zhang (2016)
Special Matrices
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A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.
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...
Li, Hsuan-Chu, Chen, Young-Ming, Tan, Eng-Tjioe (2009)
Integers
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