TY - JOUR

T1 - Multilinear functional inequalities involving permanents, determinants, and other multilinear functions of nonnegative matrices and M-matrices

AU - Goldberger, Assaf

AU - Neumann, Michael

N1 - Funding Information:
∗Corresponding author. E-mail address: [email protected] (M. Neumann). 1 Research supported in part by NSF grant no. DMS9973247.

PY - 2003/8/1

Y1 - 2003/8/1

N2 - 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.

AB - 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.

KW - Determinants

KW - M-matrices

KW - Multilinear functions

KW - Nonnegative matrices

KW - Permanents

UR - http://www.scopus.com/inward/record.url?scp=0038721117&partnerID=8YFLogxK

U2 - 10.1016/S0024-3795(02)00735-8

DO - 10.1016/S0024-3795(02)00735-8

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AN - SCOPUS:0038721117

SN - 0024-3795

VL - 369

SP - 295

EP - 310

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - SUPP.

ER -