Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 548, Issue -, Pages 42-56Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2018.02.024
Keywords
Quasi principal rank characteristic sequence; Enhanced principal rank characteristic sequence; Minor; Rank; Symmetric matrix; Schur complement
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Funding
- NSERC Discovery Research Grant, Canada [RGPIM-2014-06036. V8W 2Y2]
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A minor of a matrix is quasi-principal if it is a principal or an almost-principal minor. The quasi principal rank characteristic sequence (qpr-sequence) of an n x n symmetric matrix is introduced, which is defined as q(1)q(2) . . . qn, where q(k) is A, S, or N, according as all, some but not all, or none of its quasi-principal minors of order k are nonzero. This sequence extends the principal rank characteristic sequences in the literature, which only depend on the principal minors of the matrix. A necessary condition for the attainability of a qpr-sequence is established. Using probabilistic techniques, a complete characterization of the qpr-sequences that are attainable by symmetric matrices over fields of characteristic 0 is given. (C) 2018 Elsevier Inc. All rights reserved.
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