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A unified treatment of nearly reducible and nearly decomposable matrices. (English) Zbl 0403.15008


MSC:

15A21 Canonical forms, reductions, classification
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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References:

[1] Berge, C., Graphs and Hypergraphs (1970), Dunod: Dunod Paris · Zbl 0334.05117
[2] Bratton, D., Efficient communication networks, Cowles Comm. Disc. Paper 2119 (1955)
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[4] R. A. Brualdi, Matrices permutation equivalent to irreducible matrices and applications, to be published.; R. A. Brualdi, Matrices permutation equivalent to irreducible matrices and applications, to be published. · Zbl 0403.05016
[5] Brualdi, R. A.; Parter, S. V.; Schneider, H., The diagonal equivalence of a matrix to a stochastic matrix, J. Math. Anal. Appl., 16, 31-50 (1966) · Zbl 0231.15017
[6] Harary, F., Graph Theory (1969), Addison-Wesley: Addison-Wesley Reading, Mass. · Zbl 0797.05064
[7] Hedrick, M. B., Nearly reducible and nearly decomposable—special classes of irreducible and fully indecomposable matrices, (Thesis (1972), Unif. of Houston)
[8] Hedrick, M.; Sinkhorn, R., A special class of irreducible matrices—the nearly reducible matrices, Proc. Amer. Math. Soc., 24, 388-393 (1970) · Zbl 0198.35106
[9] Knopp, P.; Sinkhorn, R., Problems involving diagonal products in non-negative matrices, Trans. Amer. Math. Soc., 136, 67-75 (1969) · Zbl 0175.02404
[10] Gupta, R. P., On basis diagraphs, J. Combinatorial Theory, 3, 16-24 (1967) · Zbl 0149.41605
[11] Minc, H., Nearly decomposable matrices, Linear Algebra and Appl., 5, 181-187 (1972) · Zbl 0235.05008
[12] Roberts, E. J., The fully indecomposable matrix and its associated bipartite graph—an investigation of combinatorial and structural properties, NASA Technical Memorandum TM X-58037 (Jan. 1970)
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