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Linear recurrence relations in the algebra of matrices and applications |
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| Authors: | Rajae Ben Taher and Mustapha Rachidi |
| Affiliation: | a Département de Mathématiques et Informatique, Faculté des Sciences, Université Moulay Ismail, B.P. 4010, Beni M'hamed, Méknés, Morocco b Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed V, B.P. 1014, Rabat, Morocco |
| Abstract: | We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for An (nr) and etA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices Aj, where 0jr−1. |
| Keywords: | Linear recurrence relations Algebra of matrices Combinatorial expression Exponent of a matrix Exponential of a matrix |
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