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

作者：Maehara Takanori; Murota Kazuo^*

来源：Japan Journal of Industrial and Applied Mathematics, 2010, 27(2): 263-293.

DOI：10.1007/s13160-010-0007-8

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

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.

• 出版日期2010-9