Logarithm of a matrix

Summary

A logarithm of a square matrix $A$ is a matrix $B$ whose matrix exponential is $A$. Over the complex numbers, a matrix has a logarithm exactly when it is invertible. The logarithm is not unique, just as for the complex logarithm. Matrix logarithms pass from a matrix Lie group to its Lie algebra. They are also used to interpolate between rotations and to find the generator of a linear system from its flow.