Abstract
This paper is concerned with the conjecture on the permanent of the Hadamard product of two positive semidefinite matrices: per(A°B) ≤perAperB. We present some properties of correlation matrices and introduce an analytic approach of maximizing matrices for the permanent conjecture. Given an irreducible correlation matrix, we show that its maximizing matrix is (i) singular, (ii) irreducible, and (iii) invariant by a row and column reduction. © 2011 Elsevier Inc. All rights reserved.
| Original language | American English |
|---|---|
| Pages (from-to) | 1570-1579 |
| Number of pages | 10 |
| Journal | Linear Algebra and its Applications |
| Volume | 438 |
| Issue number | 4 |
| DOIs | |
| State | Published - Feb 15 2013 |
ASJC Scopus Subject Areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
Keywords
- Hadamard product
- Irreducible matrix
- Lagrange multiplier
- Maximizing matrix
- Permanent
Disciplines
- Mathematics
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