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Angle decomposition of matrices

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posted on 06.12.2019 by W.S. Verwoerd, V. Nolting
Abstract An algorithm (ADUM) is developed to decompose an arbitrary N × N unitary matrix M into 1/2N(N - 1) simple factor matrices. Each factor matrix has the form of an N × N unit matrix, except for a 2 × 2 complex rotation submatrix located at an appropriate position on the diagonal. The factor matrices each contain a rotation angle and between 0 and 3 phase angles, adding up to a total of N^2independent real angles. This can be summarized into an N × N real angle matrix Γ, containing the same inf... Title of program: adum.f Catalogue Id: ADHI_v1_0 Nature of problem The algorithm can be applied to any problem where a unitary matrix M is evaluated as a function of an external parameter. It can be generalized to a hermitian or generally complex matrix A of which this dependence is further transmitted to the eigenvector matrix M of A. Versions of this program held in the CPC repository in Mendeley Data ADHI_v1_0; adum.f; 10.1016/S0010-4655(97)00133-1 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

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