[PDF][PDF] Convex invertible cones and the Lyapunov equation
N Cohen, I Lewkowicz - Linear Algebra and its Applications, 1997 - core.ac.uk
Linear Algebra and its Applications, 1997•core.ac.uk
… Convex cones play a central role in matrix theory: the sets of Hermitian matrices or real
matrices with a prescribed sign pattern (eg entrywise positive or Z matrices) are all convex
cones. Here, we shall focus on a special family of convex cones, namely those which are
closed under matrix inver- … Our main goal in this paper is to study the Lyapunov equation
in association with matrix tics. In this section we define these mathematical objects in
general, and study their relevant properties: generating sets, nonsingularity, inertia, and …
matrices with a prescribed sign pattern (eg entrywise positive or Z matrices) are all convex
cones. Here, we shall focus on a special family of convex cones, namely those which are
closed under matrix inver- … Our main goal in this paper is to study the Lyapunov equation
in association with matrix tics. In this section we define these mathematical objects in
general, and study their relevant properties: generating sets, nonsingularity, inertia, and …
Abstract
Convex cones of matrices which are closed under matrix inversion are defined, and their structure is studied. Various connections with the algebraic Lyapunov equation of general inertia are explored. 0 Elsevier Science Inc., 1997
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