ANGLE DECOMPOSITION OF MATRICES

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.