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Zbl 0615.15008
Hill, Richard D.; Waters, Steven R.
On the cone of positive semidefinite matrices. (English)
[J] Linear Algebra Appl. 90, 81-88 (1987). ISSN 0024-3795

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.
[G.P.Barker]

MSC 2000:: *15A57 Other types of matrices
15A04 Linear transformations (linear algebra)
15A48 Positive matrices and their generalizations

Keywords: completely positive maps; invariant cone; cone of positive semidefinite Hermitian matrices; linear transformations; cone PSD; isometric isomorphisms

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