Multilinear functional inequalities involving permanents, determinants, and other multilinear functions of nonnegative matrices and M-matrices

Assaf Goldberger, Michael Neumann*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Motivated by a proof due to Fiedler of an inequality on the determinants of M-matrices and a recent paper by the authors, we now obtain various inequalities on permanents and determinants of nonsingular M-matrices. This is done by extending the multilinear considerations of Fiedler and, subsequently, of the authors, to fractional multilinear functionals on pairs of nonnegative matrices. Two examples of our results: For an n×n nonsingular M-matrix M (i) we give a sharp upper bound for det(M)+per(M), when M is a nonsingular M-matrix, (ii) we determine an upper bound on the relative error |per(M+E)-per(M)|/|per(M)|, when M+E is a certain componentwise perturbation of M.

Original languageEnglish
Pages (from-to)295-310
Number of pages16
JournalLinear Algebra and Its Applications
Volume369
Issue numberSUPP.
DOIs
StatePublished - 1 Aug 2003
Externally publishedYes

Funding

FundersFunder number
National Science FoundationDMS9973247
Directorate for Mathematical and Physical Sciences9973247

    Keywords

    • Determinants
    • M-matrices
    • Multilinear functions
    • Nonnegative matrices
    • Permanents

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