Some spectral properties of an operator associated with a pair of nonnegative matrices
Author:
M. V. Menon
Journal:
Trans. Amer. Math. Soc. 132 (1968), 369375
MSC:
Primary 15.60
MathSciNet review:
0225802
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Abstract: An operatorin general nonlinearassociated with a pair of nonnegative matrices, is defined and some of its spectral properties studied. If the pair of matrices are a square matrix A and the identity matrix of the same order, the operator reduces to the linear operator A. The results obtained include generalizations of one of the principal conclusions of the theorem of PerronFrobenius.
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 F. R. Gantmacher, The theory of matrices. II, Chelsea, New York, 1959.
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 [4]
 , Matrix links, an extremisation problem and the reduction of a nonnegative matrix to one with prescribed row and column sums, Canad. J. Math. 20 (1968), 225232. MR 0220752 (36:3804)
 [5]
 M. Morishima, Generalizations of the FrobeniusWielandt theorems for nonnegative square matrices, J. London Math. Soc. 36 (1961), 211220. MR 0124347 (23:A1661)
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 R. Sinkhorn and P. Knopp, Concerning nonnegative matrices and doubly stochastic matrices, Pacific J. Math. 21 (1967), 343348. MR 0210731 (35:1617)
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DOI:
http://dx.doi.org/10.1090/S00029947196802258022
PII:
S 00029947(1968)02258022
Article copyright:
© Copyright 1968 American Mathematical Society
