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Copositive and completely positive quadratic forms†

Published online by Cambridge University Press:  24 October 2008

Marshall Hall Jr  and
Morris Newman
Marshall Hall Jr
Affiliation:
California Institute of Technology, Pasadena, California
Morris Newman
Affiliation:
National Bureau of Standards, Washington 25, D.C.
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Extract

A copositive quadratic form is a real form which is non-negative for non-negative arguments. A completely positive quadratic form is a real form which can be written as a sum of squares of non-negative real forms. The completely positive forms are basic in the study of block designs arising in combinatorial analysis (3). The copositive forms arise in the theory of inequalities and have been considered in a paper by Mordell (4) and two papers by Diananda(1, 2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 329 - 339
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Diananda, P. H., On a conjecture of L. J. Mordell regarding an inequality involving quadratic forms. J. London Math. Soc. 36 (1961), 185–192.CrossRefGoogle Scholar
(2)Diananda, P. H., On non-negative forms in real variables some or all of which are non-negative. Proc. Cambridge Philos. Soc. 58 (1962), 17–25.CrossRefGoogle Scholar
(3)Hall, , Marshall, Jr., Discrete problems. A Survey of Numerical Analysis, ed. John, Todd, (McGraw-Hill, New York, 1962) pp. 518–542.Google Scholar
(4)Mordell, L. J., On the inequality and some others. Abh. Math. Sem. Univ. Hamburg, 22 (1958), 229–240.CrossRefGoogle Scholar
(5)Motzkin, T., Copositive quadratic forms. National Bureau of Standards Report 1818 (1952), pp. 11–12.Google Scholar