Scientific computing related to the pth root and the logarithm of a matrix

M. Bakherad, D. Yaqubi, H. Kamali

In this paper, we present significant results regarding the logarithm and the pth root of a substantial collection of linear transformations known as annihilated linear transformations, and specifically for any matrix. We employ difference equations to compute any power of an annihilated linear transformation T, providing a clear approach to calculate the pth root and the logarithm of a non-singular square matrix A. Our computations are conducted with precision and are exact, rather than relying on numerical approximations. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(2) (2026), pp. 1-18