Linear preservers of copositive matrices

• Type: Article in International Scientific Journal
• Date: 2021-06-27

Authors

Susana Borges Furtado (Author) FEP; Johnson, CR (Author) Other; Zhang, YL (Author) Other

Journal

Title: Linear and Multilinear Algebra

Vol. 69

Pages: 1779-1788

ISSN: 0308-1087

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00R-DKC

DOI: 10.1080/03081087.2019.1692775

Abstract (EN): An n-by-n real symmetric matrix is called copositive if its quadratic form is nonnegative on nonnegative vectors. Our interest is in identifying which linear transformations on symmetric matrices preserve copositivity either in the into or onto sense. We conjecture that in the onto case, the map must be congruence by a monomial matrix (a permutation times a positive diagonal matrix). This is proven under each of some additional natural assumptions. Also, the into preservers of standard type are characterized. A general characterization in the into case seems difficult, and examples are given. One of them provides a counterexample to a conjecture about the into preservers.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10