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| In mathematics, specifically ], a ] ''A'' is '''copositive''' if | In mathematics, specifically ], a ] ] ''A'' is '''copositive''' if | ||
| :<math>x^TAx\geq 0</math> | :<math>x^TAx\geq 0</math> | ||
| for every nonnegative vector <math>x\geq 0</math>. The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real ]. | for every nonnegative vector <math>x\geq 0</math>. The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real ]. | ||
Revision as of 00:15, 17 February 2017
In mathematics, specifically linear algebra, a real matrix A is copositive if
for every nonnegative vector . The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real positive-definite matrices.
. The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real Copositive matrices find applications in economics, operations research, and statistics.
References
- Berman, Abraham; Robert J. Plemmons (1979). Nonnegative Matrices in the Mathematical Sciences. Academic Press. ISBN 0-12-092250-9.
- Copositive matrix at PlanetMath