Analytic function of a matrix

An analytic function of a matrix is a generalization of the concept of analytic functions from complex analysis to the setting of matrices. In complex analysis, a function \( f(z) \) is called analytic at a point \( z_0 \) if it can be represented by a power series around \( z_0 \). In a similar way, when we talk about matrices, we consider functions that can be expressed as power series in terms of matrices.