Vol. 15, No. 2, 1965

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Reduction of sets of matrices to a triangular form

Indranand Sinha

Vol. 15 (1965), No. 2, 673–679

A set Ω of n × 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 Ω-decomposition into primary components; i.e. V = V 1 V t, where the restrictions of the elements of Ω to any V i are primary linear transformations; and (ii) V has an Ω-composition series with 1-dimensional composition-factors.

Our aim in this paper will be to characterize sets of nonsingular linear transformations having Property T.

Mathematical Subject Classification
Primary: 14.50
Secondary: 20.75
Received: 3 December 1963
Revised: 25 March 1964
Published: 1 June 1965
Indranand Sinha