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Linear mappings preserving the copositive cone.
- Source :
- Proceedings of the American Mathematical Society; Aug2021, Vol. 149 Issue 8, p3173-3176, 4p
- Publication Year :
- 2021
-
Abstract
- Let S<subscript>n</subscript> be the set of all n-by-n symmetric real matrices, and let C<subscript>n</subscript> be the copositive cone, that is, the set of all matrices a ∈ S<subscript>n</subscript> that fulfill the condition u<superscript>top</superscript> a u ≥ 0 for all n-vectors u with nonnegative entries. We prove that a linear mapping φ : S<subscript>n</subscript> → S<subscript>n</subscript> satisfies φ (C<subscript>n</subscript>)= C<subscript>n</subscript> if and only if φ (x)=m<superscript>top</superscript> xm for a fixed monomial matrix m with nonnegative entries. [ABSTRACT FROM AUTHOR]
- Subjects :
- LINEAR operators
SYMMETRIC matrices
CONES
MATRICES (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 149
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 150690133
- Full Text :
- https://doi.org/10.1090/proc/15432