ANGLE DECOMPOSITION OF MATRICES

Citation
Ws. Verwoerd et V. Nolting, ANGLE DECOMPOSITION OF MATRICES, Computer physics communications, 108(2-3), 1998, pp. 218-239
Citations number
7
Categorie Soggetti
Computer Science Interdisciplinary Applications","Physycs, Mathematical","Physycs, Mathematical","Computer Science Interdisciplinary Applications
ISSN journal
00104655
Volume
108
Issue
2-3
Year of publication
1998
Pages
218 - 239
Database
ISI
SICI code
0010-4655(1998)108:2-3<218:ADOM>2.0.ZU;2-Y
Abstract
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.