In MATLAB®, the functions
sqrtm compute the matrix exponential, matrix logarithm, and matrix square root, respectively. The matrix exponential plays a role in the solution of systems of ordinary differential equations. The matrix logarithm and matrix square root are perhaps less commonly used, but that does not mean they are not useful.
In this article, originally published in 1993, Cleve Moler explores the mathematics behind these functions and their inverses using some surprising examples.