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In a recent paper, a new method was proposed to find the common invariantsubspaces of a set of matrices. This paper invstigates the more general problemof putting a set of matrices into block triangular or block-diagonal formsimultaneously. Based on common invariant subspaces, two algorithms forsimultaneous block triangularization and block diagonalization of sets ofmatrices are presented. As an alternate approach for simultaneous blockdiagonalization of sets of matrices by an invertible matrix, a new algorithm isdeveloped based on the generalized eigen vectors of a commuting matrix.Moreover, a new characterization for the simultaneous block diagonalization byan invertible matrix is provided. The algorithms are applied to concreteexamples using the symbolic manipulation system Maple.

Algorithms for Simultaneous Block Triangularization and Block Diagonalization of Sets of Matrices