We prove that an operator generates a positive group on the real space of real or complex Hermitian matrices, if and only if it is a Lyapunov operator. In particular it follows that every group of positive operators in fact is a group of completely positive operators.
โฆ LIBER โฆ
Complete positive group presentations
โ Scribed by Patrick Dehornoy
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 517 KB
- Volume
- 268
- Category
- Article
- ISSN
- 0021-8693
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An n ร 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 ร 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 conditi