Simultaneous reduction of sets of matrices under similarity

Abstract

AbstractLet S be a set of n × n matrices over a field F, and A the algebra generated by S over F. The problem of deciding whether the elements of S can be simultaneously reduced (to block-triangular form with the diagonal blocks of some specified size) is considered, and an account is given of various methods used to attack the problem. Most of the techniques use representation theory to obtain information on A. The problems of simultaneous triangularization, existence of common eigenvectors, etc. are also considered. The aim of the paper is to survey the methods used to attack these problems and to give some typical results. The paper does not contain many new results