Abstract
Functions with matrix arguments represent a mathematical generalization of functions of numerical arguments. Of particular interest is the determination of functions of matrices and the calculation of their values, primarily in connection with the solutionof applied problems. It is possible to minimise the computational complexity, which is related not only to the increase in the order of the matrix but also to the presence of simple and multiple roots of the matrix's characteristic polynomial, by performing such computations in modern computer mathematics software packages. The present article develops code for computing a function with a matrix argument, in the case of simple roots of the matrix's characteristic polynomial, in the Maple system.