Characterizations of rectangular totally and strictly totally positive matrices

An n × m real matrix A is said to be totally positive (strictly totally positive) if every minor is nonnegative (positive). In this paper, we study characterizations of these classes of matrices by minors, by their full rank factorization and by their thin QR factorization.

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Bibliographic Details
Published inLinear algebra and its applications Vol. 432; no. 10; pp. 2623 - 2633
Main Authors Cantó, Rafael, Ricarte, Beatriz, Urbano, Ana M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.05.2010
Elsevier
Subjects
Algebra
Exact sciences and technology
Full rank factorization
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Thin [formula omitted] factorization
Totally positive and strictly totally positive matrices
65F40
15A15
Full rank factorization
Thin QR factorization
15A23
Totally positive and strictly totally positive matrices
Totally positive and strictly totally positive
Matrix factorization
Matrix function
Rectangular matrix
Non negative matrix
QR factorization
Minor
matrices
Positive operator
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Summary:An n × m real matrix A is said to be totally positive (strictly totally positive) if every minor is nonnegative (positive). In this paper, we study characterizations of these classes of matrices by minors, by their full rank factorization and by their thin QR factorization.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2009.12.004