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Positive groups on Hn are completely positive

✍ Scribed by Tobias Damm

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
198 KB
Volume
393
Category
Article
ISSN
0024-3795

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Notes on completely positive matrices
Notes on completely positive matrices
✍ Shuhuang Xiang; Shuwen Xiang πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 326 KB

Let A be a n Γ— n symmetric matrix and in the closure of inverse M-matrices. Then A can be factored as A = BB r for some nonnegative lower triangular n Γ— n matrix B, and cp-rank A ~< n. If A is a positive semidefinite (0, 1) matrix, then A is completely positive and cp-rank A = rank A; if A is a non