Explicit formulas for the exponentials of some special matrices (Q628258)

Explicit formulas to compute \(e^A\) are given for square complex matrices \(A\) satisfying \(A^{k+1}=\rho A\), \(A^{k+2}=\rho A\), or \(A^{k+3}=\rho A\) for a fixed nonnegative integer \(k\) and a constant \(\rho\). The method used in this paper is the polynomial methods of \textit{C. Moler} and \textit{C. Van Loan} [SIAM Rev. 45, No. 1, 3--49 (2003; Zbl 1030.65029)]. The proofs are easy.