On the necessity and sufficiency of $$PLUS$$ factorizations.(English)Zbl 1071.15012

A $$PLUS$$ factorization for an arbitrary nonsingular $$n\times n$$ matrix $$A$$ has the form $$A=PLUS$$, where $$P$$ is a permutation matrix, $$L$$ is a unit lower triangular matrix, $$U$$ is an upper triangular matrix whose diagonal entries are prescribed as long as the determinant is equal to that of $$A$$ up to a possible sign adjustment, and $$S$$ is a unit lower triangular matrix of which all but $$n-1$$ off-diagonal entries are zeros and the positions of those $$n-1$$ entries are also flexibly customizable.
The authors show that the necessary condition for the existence of a $$PLUS$$ factorization of a matrix $$A$$ as given by P. Hao [ibid. 382, 135–154 (2004; Zbl 1050.15012)] is not sufficient and they find a sufficient condition for such a factorization.

MSC:

 15A23 Factorization of matrices

Zbl 1050.15012
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References:

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