Some explicit formulas for the polynomial decomposition of the matrix exponential and applications
Formulas for the polynomial decomposition of the exponential of a square matrix \(A\), by considering the Jordan normal form of \(A\), are studied. The exponential \(e^{iA}\) is given in terms of \(P_0(A),\dots,P_{m-1} (A) \), where the \(P_j(A)\) are polynomials in \(A\) of degree less than \(m\). The cases with \(m=5\) and \(m=6\) are discussed in detail. The results are also compared with those derived by the authors previously [ibid. 330, No. 1-3, 15-24 (2001; Zbl 0983.15018)].
scientific article; zbMATH DE number 1790263
scientific article