Matrix function

Summary

A matrix function extends a scalar function $f$ to square matrices, giving a matrix $f(A)$ for a matrix $A$. For a function given by a power series, $f(A)$ is obtained by putting $A$ into the series. The matrix exponential, the logarithm of a matrix and the square root of a matrix are the main examples. They are used to solve linear differential equations and in numerical analysis, control theory and quantum mechanics.