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Factorizations of completely positive matrices

Published online by Cambridge University Press:  24 October 2008

Thomas L. Markham
Affiliation:
University of South Carolina

Extract

1. Introduction. DEFINITION. If with aij = aji, is a real quadratic form inx1 …,xn, andwhere Lk = cklx1 + … + cknxn (ckj ≥ 0 for k = 1, …, t), then Q is called a completely positive form, and A = (aij) is called a completely positive matrix.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Diananda, P. H.On non-negative forma in real variables some or all of which are nonnegative. Proc. Cambridge Philos. Soc. 58 (1962), 1725.CrossRefGoogle Scholar
(2)Gantmacher, F. and Krein, M.Sur les matrices complèment non négatives et oscillatoires. Compoaitio Math. 4 (1937), 445476.Google Scholar
(3)Hall, M. and Newman, M.Copositive and completely positive quadratic forms. Proc. Cambridge Philos. Soc. 59 (1963), 329339.CrossRefGoogle Scholar
(4)Haynsworth, E. V.Determination of the inertia of a partitioned Hermitian matrix. Linear algebra and its applications 1 (1968), 7381.CrossRefGoogle Scholar
(5)Haynsworth, E. V. and Crabtree, D.An identity for the Schur complement of a matrix. Proc. Amer. Math. Soc. 22 (1969), 364366.Google Scholar
(6)Motzkin, T.Copositive quadratic forms. National Bureau of Standards Report 1818 (1952), 1112.Google Scholar