Reduction of sets of matrices to a triangular form
Indranand Sinha · Pacific Journal of Mathematics · 1965
A set Ω of n X n matrices is said to have Property T if the following two conditions are satisfied: (i) If Ω is looked upon as a set of linear transformations of a vector space V of dimension n then V has an ^-decomposition into primary components; i. e. V -VΊ 0 0 Vt 9 where the restrictions of the elements of Ω to any V% are primary linear transformations; and (ii) V has an ^-composition series with 1-dimensional composition-factors.Our aim in this paper will be to characterize sets of nonsingular linear transformations having Property T.