Physical Sciences and Mathematics Commons^™

Computing A Logarithm Of A Unitary Matrix With General Spectrum [Dataset], Terry A. Loring

Math and Statistics Datasets

We analyze an algorithm for computing a skew-Hermitian logarithm of a unitary matrix, and also skew-Hermitian approximate logarithms for nearly unitary matrices. This algorithm is very easy to implement using standard software and it works well even for unitary matrices with no spectral conditions assumed. Certain examples, with many eigenvalues near -1, lead to very non-Hermitian output for other basic methods of calculating matrix logarithms. Altering the output of these algorithms to force an Hermitian output creates accuracy issues which are avoided by the considered algorithm. A modification is introduced to deal properly with the J-skew symmetric unitary matrices. Applications …