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Theorems of the alternative for cones and Lyapunov regularity of matrices

Bryan CainDaniel HershkowitzHans Schneider — 1997

Czechoslovak Mathematical Journal

Standard facts about separating linear functionals will be used to determine how two cones C and D and their duals C * and D * may overlap. When T V W is linear and K V and D W are cones, these results will be applied to C = T ( K ) and D , giving a unified treatment of several theorems of the alternate which explain when C contains an interior point of D . The case when V = W is the space H of n × n Hermitian matrices, D is the n × n positive semidefinite matrices, and T ( X ) = A X + X * A yields new and known results about the existence of block diagonal...

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