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Bipartite completely positive matrices

Published online by Cambridge University Press:  24 October 2008

Abraham Berman  and
Robert Grone
Abraham Berman
Affiliation:
Departments of Mathematics, Technion-Israel Institute of Technology, Haifa 32000 Israel, and University of California at San Diego, La Jolla, CA 92093, U.S.A.
Robert Grone
Affiliation:
Department of Mathematical Sciences, San Diego State University, San Diego, CA 92182, U.S.A.
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Extract

A non-zero n-by-n matrix A is said to be completely positive if there exist non-negative vectors b1,…, bk, such that

The smallest such integer k is called the factorization index of (completely positive) A, and is denoted by ø(A). Completely positive matrices are important in the study of block designs [4], statistics and modelling of energy demand [3].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 269 - 276
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Berman, A. and Hershkowitz, D.. Combinatorial results on completely positive matrices. To appear in Lin. Alg. Appl.Google Scholar
[2]Coulson, C. A. and Rushbrooke, G. S.. Note on the method of molecular orbitals. Proc. Cambridge Philos. Soc. 36 (1940), 193–200.CrossRefGoogle Scholar
[3]Gray, L. J. and Wilson, D. G.. Nonnegative factorization of positive semidefinite nonnegative matrices. Lin. Alg. Appl. 31(1980), 119–127.CrossRefGoogle Scholar
[4]Hall, M. Jr,. Combinatorial Theory, 2nd ed. (Wiley, 1986).Google Scholar
[5]Hall, M. Jr,. and Newman, M.. Copositive and completely positive quadratic forms. Proc. Cambridge Philos. Soc. 59 (1963), 329–339.CrossRefGoogle Scholar
[6]Hannah, J. and Laffey, T. J.. Nonnegative factorization of completely positive matrices. Lin. Alg. Appl. 55 (1983), 1–9.CrossRefGoogle Scholar
[7]Markham, T. L.. Factorization of completely positive matrices. Proc. Cambridge Philos. Soc. 69 (1971), 53–58.CrossRefGoogle Scholar