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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×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:
15A57Other types of matrices (MSC2000)
15A04Linear transformations, semilinear transformations (linear algebra)
15A48Positive matrices and their generalizations (MSC2000)