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Generalized eigenvectors and sets of nonnegative matrices. (English) Zbl 0548.15015
Let K be the finite set of square non-negative matrices with index set \(\{\) 1,2,...,\(N\}\) with the ”product property”: that for each \(i=1,...,N\) there exists a collection C(i) of non-negative row vectors of length N, and the elements of K are constructed by selecting the ith from C(i), \(i=1,...,N\), all possible combinations being taken. The structural properties of the class K are studied in a manner developed from the approach of P. Mandl and the reviewer [Aust. J. Stat. 11, 85-96 (1969; Zbl 0185.080)] in a dynamic programming context; and the spectral approach of U. G. Rothblum [Linear Algebra Appl. 12, 281-292 (1975; Zbl 0321.15010)] for one matrix.
Reviewer: E.Seneta

MSC:
15B48 Positive matrices and their generalizations; cones of matrices
15A18 Eigenvalues, singular values, and eigenvectors
90C30 Nonlinear programming
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