Multilinear functional inequalities involving permanents, determinants, and other multilinear functions of nonnegative matrices and M-matrices
✍ Scribed by Assaf Goldberger; Michael Neumann
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 168 KB
- Volume
- 369
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
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.