Vol. 40, No. 1, 1972

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Diagonal similarity of irreducible matrices to row stochastic matrices

Darald Joe Hartfiel and J. W. Spellmann

Vol. 40 (1972), No. 1, 97–99
Abstract

By using the Perron-Frobenius Theorem it is easily shown that if A is an irreducible matrix then there is a diagonal matrix D with positive main diagonal so that DAD1 = rS where r is a positive scalar and S a stochastic matrix. This paper gives a short proof of this result without direct appeal to the Perron-Frobenius Theorem.

Mathematical Subject Classification 2000
Primary: 15A21
Milestones
Received: 4 December 1970
Revised: 6 May 1971
Published: 1 January 1972
Authors
Darald Joe Hartfiel
J. W. Spellmann