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- W2616164512 abstract "Abstract Let A be an element of the copositive cone C n . A zero u of A is a nonzero nonnegative vector such that u T A u = 0 . The support of u is the index set supp u ⊂ { 1 , … , n } corresponding to the positive entries of u . A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u . We investigate the properties of minimal zeros of copositive matrices and their supports. Special attention is devoted to copositive matrices which are irreducible with respect to the cone S + ( n ) of positive semi-definite matrices, i.e., matrices which cannot be written as a sum of a copositive and a nonzero positive semi-definite matrix. We give a necessary and sufficient condition for irreducibility of a matrix A with respect to S + ( n ) in terms of its minimal zeros. A similar condition is given for the irreducibility with respect to the cone N n of entry-wise nonnegative matrices. For n = 5 matrices which are irreducible with respect to both S + ( 5 ) and N 5 are extremal. For n = 6 a list of candidate combinations of supports of minimal zeros which an exceptional extremal matrix can have is provided." @default.
- W2616164512 created "2017-05-26" @default.
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- W2616164512 date "2014-06-29" @default.
- W2616164512 modified "2023-09-26" @default.
- W2616164512 title "Minimal zeros of copositive matrices" @default.
- W2616164512 hasPublicationYear "2014" @default.
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