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  • Direct approach to rank-1 completions of partial matrices
    Cigler, Gregor ; Wojciechowski, Piotr J.
    Given a rectangular matrix with some missing entries, the possibility of their completion, specific to some desired requirements, has been of interest for the last few decades. As a result, powerful ... tools, numerous algorithms and applications in several areas have flourished in the literature. In the current note we take a direct, elementary approach to some aspects of completion of a partial matrix to one of rank 1. Our methods do not go beyond basic linear algebra. We introduce the natural concept of a rank 1-like matrix. An equivalence is shown between completions of some special matrices and completions of transitive systems. Our main theorem states that a rectangular matrix can be completed if and only if all of its square submatrices can be completed to rank 1 matrices.
    Source: Mathematical proceedings of the Royal Irish Academy. - ISSN 1393-7197 (Vol. 122A, no. 2, 2022, str. 87-99)
    Type of material - article, component part ; adult, serious
    Publish date - 2022
    Language - english
    COBISS.SI-ID - 178100739

    Link(s):

    https://muse.jhu.edu/pub/423/article/864447
    DOI

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