Reducibility theorems for pairs of matrices as rational criteria (Q1579521)

The authors give a more tractable approach to ``classical'' theorems of \textit{N. H. McCoy} [Bull. Am. Math. Soc. 42, 592-600 (1936; Zbl 0015.05501)], \textit{H. Shapiro} [Linear Algebra Appl. 25, 129-137 (1979; Zbl 0401.15008)] and \textit{J. F. Watters} [Linear Algebra Appl. 9, 103-117 (1974; Zbl 0292.15004)] related to simultaneous reduction to a special form (e.g. block triangular or diagonal form) of a pair (or set) of matrices, by showing that we only have to do a finite number of operations in order to verify the hypotheses of the theorems. In the appendix, they give an extension ``à la Shapiro'' of the McCoy theorem.