Matrixes Satisfying Siljak’s Conjecture

Abstract

Siljak’s Conjecture on the existence of a symmetric positive definite matrix V having a specified structure and satisfying Liapunov’s matrix equation A*V+VA= -W is shown to be true in cases when A is an orthogonal matrix; when A is a symmetric matrix; when A is a normal matrix or A is the linear combination of nonnegative coefficient of all these matrixes