On the matrix powers and exponential by the \(r\)-generalized Fibonacci sequences methods: The companion matrix case

DOI10.1016/S0024-3795(03)00418-XzbMath1031.15019MaRDI QIDQ1405048

Mustapha Rachidi, Rajae Ben Taher

Publication date: 25 August 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

companion matrixalgebra of matriceslinear recurrence relationsmatrix exponentialdynamical solutionmatrix powersFibonacci sequences methods

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Eigenvalues, singular values, and eigenvectors (15A18) Algebraic systems of matrices (15A30) Approximation to limiting values (summation of series, etc.) (40A25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

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Cites Work

• On functions of companion matrices
• More explicit formulas for the matrix exponential
• Some explicit formulas for the polynomial decomposition of the matrix exponential and applications
• The combinatorial power of the companion matrix
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• Linear fractional transforms of companion matrices
• Classroom Note:A Note on the Matrix Exponential
• Operator Identities and the Solution of Linear Matrix Difference and Differential Equations
• The Matrix Exponential
• Linear recurrence relations in the algebra of matrices and applications
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