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    Combinatorial aspects of rectangular non-negative matrices

    Fenner, Trevor and Loizou, G. (1977) Combinatorial aspects of rectangular non-negative matrices. Discrete Mathematics 20 , pp. 217-234. ISSN 0012-365X.

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    Fully indecomposable and essentially non-singular rectangular matrices are defined together with several similar, but more general, classes of matrices. We define the submatrix nullity of a matrix to be the maximal sum of the dimensions, taken over all non-vacuous zero submatrices, and also introduce a complementary quantity, the cover rank, which is an extension of the term rank. Properties of the various classes of matrices are investigated, and various characterisations of these classes are derived. Bounds on the submatrix nullity and the cover rank of the product of two non-negative matrices are obtained, and the problem of classifying the product into the various classes is investigated.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hall
    Date Deposited: 23 Mar 2021 20:05
    Last Modified: 09 Aug 2023 12:50


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