On the cone of positive semidefinite matrices. (English) Zbl 0615.15008
An as yet unsolved problem in matrix theory is to classify those linear transformations of the \(n\times n\) complex matrices which leave the cone, PSD, of positive semidefinite Hermitian matrices invariant. The present note surveys the known results on the structure of the cone PSD, and some of the results concerning linear transformations which map PSD into itself. Certain useful isometric isomorphisms are given in detail.
Reviewer: G.P.Barker
MSC:
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
| 15A04 | Linear transformations, semilinear transformations |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
Keywords:
completely positive maps; invariant cone; cone of positive semidefinite Hermitian matrices; linear transformations; cone PSD; isometric isomorphismsReferences:
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