Complete positivity of matrices of special form. (English) Zbl 0977.15013
Conditions for the complete positivity of positive semidefinite matrices are extended by considering doubly nonnegative matrices of a special block form. The characterizations give conditions under which an entrywise nonnegative positive semi-definite matrix \(A\) with a special block form can be written as \(A=BB^T\) \((B\) is entrywise nonnegative). The decompositions of doubly nonnegative matrices in the \(2\times 2\) case, in the \(n\times n\) case, and applications to complete positivity are discussed.
Reviewer: Václav Burjan (Praha)
MSC:
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 15A23 | Factorization of matrices |
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