Vol. 35, No. 1, 1970

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On matrices with a restricted number of diagonal values

J. E. H. Elliott

Vol. 35 (1970), No. 1, 79–82
Abstract

This note confirms the following conjecture of Marcus: Let A = (aij) be an n × n matrix of strictly positive entries with at most (n 1) distinct diagonal values, then A is singular. We also show that there exist matrices with strictly positive entries with n diagonal values which are nonsingular.

Mathematical Subject Classification
Primary: 15.05
Milestones
Received: 25 July 1968
Published: 1 October 1970
Authors
J. E. H. Elliott