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Completely positive matrices

✍ Scribed by Changqing Xu

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
178 KB
Volume
379
Category
Article
ISSN
0024-3795

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✦ Synopsis

An n Γ— n real matrix A is called completely positive (CP) if it can be factored as A = B B (" " stands for transpose) where B is an m Γ— n entrywise nonnegative matrix for some integer m. The smallest such number m is called the cprank of A. In this paper we present a necessary and sufficient condition for any entrywise nonnegative and positive semidefinite matrix to be CP. We also present an expression for the cprank of any CP matrix.

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