Generalization of Flanders' theorem to matrix triples

This paper deals with several ways to generalize the Flanders' theorem to matrix triples. We consider six invertible matrices and try to write them as the possible products of three matrices. Initially, we describe a wide set of necessary conditions so that this system be solvable, showing that they are not sufficient. Next, we study the simultaneous solvability of two equations, selected appropriately among the matrix system. The rest of the paper is devoted to the study of a particular case, in which the six given matrices are simultaneously diagonalizable, with distinct nonzero eigenvalues. In this case, we obtain a necessary and sufficient condition for the solvability of the full matrix system. Moreover, an explicit solution to it is constructed. Certain technical results necessary for this work may be of independent interest. (C) 2003 Elsevier Inc. All rights reserved.