Abstract
Various methods have been introduced for calculating the matrix sine and cosine. This paper concerns the Fibonacci-Horner decomposition of the matrix sine and cosine sin(tA), cos(tA) (A ∈ M (r; ℂ), t ∈ ℝ), which is derived from the combinatorial properties of the generalized Fibonacci sequences in the algebra of square matrices. Finally we derive some formulas for the trigonometric functions of f(A) where f is an homographic function.
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