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Note On a Matrix Theorem Of A. Brauer and its Extension

Published online by Cambridge University Press:  20 November 2018

L. S. Goddard
L. S. Goddard*
Affiliation:
King's College, Aberdeen
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1. Introduction. In one of his papers on limits for the characteristic roots of a Matrix, Brauer (1) has stated a theorem, which connects the roots of a given square matrix A, with those of a matrix A* derived from A by a certain process. The proof of this theorem involves a continuity argument and in a recent paper on the construction of stochastic matrices Hazel Perfect (5) has given a proof which avoids considerations of continuity.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 527 - 530
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Brauer, A., Limits for the characteristic roots of a matrix IV: Applications to stochastic matrices, Duke Math. J., 19 (1952), 75.Google Scholar
2. Drazin, M. P., Dungey, J. W., and Gruenberg, K. W., Some theorems on commutative matrices, J. Lond. Math. Soc, 26 (1951), 221.Google Scholar
3. Goddard, L. S. and Schneider, H., Pairs of matrices with a non-zero commutator, Proc. Cambridge Phil. Soc, 51 (1955).Google Scholar
4. McCoy, N. H., On the characteristic roots of matrix polynomials, Bull. Amer. Math. Soc, 42 (1936), 592.Google Scholar
5. Perfect, H., Methods of constructing certain stochastic matrices, Duke Math. J., 20 (1953), 395.Google Scholar