An algorithm (ADUM) is developed to decompose an arbitrary N x N unita
ry matrix M into 1/2N(N-1) simple factor matrices. Each factor matrix
has the form of an N x N unit matrix, except for a 2 x 2 complex rotat
ion submatrix located at an appropriate position on the diagonal. The
factor matrices each contain a rotation angle and between 0 and 3 phas
e angles, adding up to a total of N-2 independent real angles. This ca
n be summarized into an N x N real angle matrix Gamma, containing the
same information as the unitary matrix M. The factorisation can be ext
ended to Hermitian or even generally complex matrices by applying an e
igenvalue expansion or, alternatively, a singular value decomposition.
Several applications to physical problems are discussed, and it is sh
own that ADUM is a powerful tool in the interpolation of matrices whic
h depend on external parameters because it efficiently represents the
degrees of freedom of a matrix while guaranteeing that matrix properti
es are maintained. (C) 1998 Elsevier Science B.V.