Sweeping-similarity of matrices (Q1071087)

This paper is partly expository. It deals with a canonical form problem for finite sets of matrices and generalizes matrix equivalence, matrix similarity, and simultaneous equivalence of pairs of matrices. A generalization of some more complicated matrix problems of the work of \textit{L. A. Nazarova} and \textit{A. V. Rojter} [Izv. Akad. Nauk SSSR, Ser. mat. 33, 65-89 (1969; Zbl 0195.043)] is also included. The paper contains sections of introductions, canonical form, applications, decomposition theorem, invariants of deleted and block cycles, and a Krull-Schmidt theorem.