EUDML

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 $T V \to W$ is linear and $K \subset V$ and $D \subset W$ 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 $n \times n$ Hermitian matrices, $D$ is the $n \times n$ 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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$P^{α}$ -matrices and Lyapunov scalar stability.

Spectral properties of sign symmetric matrices.

On nonnegative sign equivalent and sign similar factorizations of matrices.

One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices.

Positive entries of stable matrices.

Sequences, wedges and associated sets of complex numbers

Forcing sequences of positive integers

On the minimum rank of not necessarily symmetric matrices: a preliminary study.

Theorems of the alternative for cones and Lyapunov regularity of matrices