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Zbl 0534.15012
Barker, George Phillip; Hill, Richard D.; Haertel, Raymond D.
On the completely positive and positive-semidefinite-preserving cones. (English)
[J] Linear Algebra Appl. 56, 221-229 (1984). ISSN 0024-3795

Let $M\sb n$, $H\sb n$, and $P\sb n$ be respectively the complex space of $n\times n$ complex matrices, the real space of Hermitian matrices in $M\sb n$, and the cone of positive semidefinite matrices in $H\sb n$. The authors show that the cone $CP\sb{n,q}$ of completely positive linear maps from $M\sb n$ to $M\sb q$ is isometrically isomorphic to the cone $P\sb{nq}$, and identify certain right and left facial ideals in $CP\sb{n,n}$. They define a joint angular field of values of a sequence $K\sb 1,...,K\sb m$, $K\sb i\in H\sb n$, and use it to characterize when a sum of dyad products $\sum\sp{m}\sb{i=1}K\sb i\otimes L\sb i$, $K\sb i\in H\sb n$, $L\sb i\in H\sb q$, preserves semidefiniteness.
[D.Carlson]

MSC 2000:: *15A48 Positive matrices and their generalizations
06F20 Ordered abelian groups, etc.

Keywords: completely positive; positive-semidefinite-preserving cones; hermitian- preserving; left and right facial ideals; joint angular field of values

Cited in: Zbl 0573.15001

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