Some spectral properties of an operator associated with a pair of nonnegative matrices

Menon, M. V.

doi:10.1090/S0002-9947-1968-0225802-2

Some spectral properties of an operator associated with a pair of nonnegative matrices
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by M. V. Menon

Trans. Amer. Math. Soc. 132 (1968), 369-375

DOI: https://doi.org/10.1090/S0002-9947-1968-0225802-2

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Abstract:

An operator—in general nonlinear—associated with a pair of non-negative 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 Perron-Frobenius.

References

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The theory of matrices

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