A cone associated with the Lyapunov mapping Public Deposited

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  • In this paper we investigate the Lyapunov mapping P --> AP + PA * where A is a positive stable matrix and P is a hermitian matrix. In particular, for special positive stable A we characterize the image of the cone of positive definite matrices under this mapping. In Section V we give five conditions on an nXn hermitian matrix H and a general nXn positive stable matrix A. that are equivalent to the condition: H = AP + PA* for some positive definite (hermitian) P.
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