Japan Journal of Industrial and Applied Mathematics

, Volume 27, Issue 2, pp 263–293

A numerical algorithm for block-diagonal decomposition of matrix *-algebras with general irreducible components

Original Paper Area 2

DOI: 10.1007/s13160-010-0007-8

Cite this article as:
Maehara, T. & Murota, K. Japan J. Indust. Appl. Math. (2010) 27: 263. doi:10.1007/s13160-010-0007-8


An algorithm is proposed for finding the finest simultaneous block-diagonalization of a finite number of square matrices, or equivalently the irreducible decomposition of a matrix *-algebra given in terms of its generators. This extends the approach initiated by Murota–Kanno–Kojima–Kojima. The algorithm, composed of numerical-linear algebraic computations, does not require any algebraic structure to be known in advance. The main ingredient of the algorithm is the Schur decomposition and its skew-Hamiltonian variant for eigenvalue computation.


Matrix *-algebra Block-diagonalization Group symmetry Schur decomposition Skew-Hamiltonian Schur decomposition 

Copyright information

© The JJIAM Publishing Committee and Springer 2010

Authors and Affiliations

  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan

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