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Direct approach to rank-1 completions of partial matricesCigler, 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, seriousPublish date - 2022Language - englishCOBISS.SI-ID - 178100739
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Cigler, Gregor |
Wojciechowski, Piotr J.
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source: Mathematical proceedings of the Royal Irish Academy. - ISSN 1393-7197 (Vol. 122A, no. 2, 2022, str. 87-99)
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Cigler, Gregor | 13430 |
Wojciechowski, Piotr J. | ![]() |
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