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Transposable and symmetrizable matrices

Part of: Designs and configurations Graph theory

Published online by Cambridge University Press:  09 April 2009

David McCarthy  and
Brendan D. McKay
David McCarthy
Affiliation:
Department of Computer Science University of ManitobaWinnipeg, Manitoba R3T 2N2, Canada
Brendan D. McKay
Affiliation:
Department of Mathematics University of MelbourneParkville, Victoria 3052, Australia
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Abstract

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A square matrix A is transposable if P(RA) = (RA)T for some permutation matrices p and R, and symmetrizable if (SA)T = SA for some permutation matrix S. In this paper we find necessary and sufficient conditions on a permutation matrix P so that A is always symmetrizable if P(RA) = (RA)T for some permutation matrix R.

MSC classification

Secondary: 05B20: Matrices (incidence, Hadamard, etc.) 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 469 - 474
Copyright
Copyright © Australian Mathematical Society 1980

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