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Completions of M-matrix patterns

✍ Scribed by Leslie Hogben

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 624 KB
Volume: 285
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10120-9

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✦ Synopsis

A list of positions in an n x n real matrix (a pattern) is said to have M-completion if every partial M-matrix that specifies exactly these positions can be completed to an Mmatrix. Let Q be a pattern that includes all diagonal entries and let G be its digraph. The following are equivalent. (1) the pattern Q has M-completion; (2) the pattern Q is permutation similar to a block triangular pattern with all the diagonal blocks completely specified; (3) any strongly connected subdigraph of G is complete. A pattern with some diagonal entries unspecified has M-completion if and only if the principal subpattern defined by the specified diagonal positions has M-completion.

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