On an Analogue of a Property of Singular M-matrices, for the Lyapunov and the Stein Operators

2023/05/07 by Encinas, A. M., Mondal, Samir, Sivakumar, K. C.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2305.04932

Abstract

In the setting of real square matrices, it is known that, if A is a singular irreducible M-matrix, then the only nonnegative vector that belongs to the range space of A is the zero vector. In this paper, we prove an analogue of this result for the Lyapunov and the Stein operators.

Related

• The Strong Singular Value Property for Matrices
• A note on a conjecture concerning rank one perturbations of singular M-matrices
• Singular Vectors in Real Affine Subspaces
• A note on algebraic Riccati equations associated with reducible singular M-matrices
• A Hill-Pick matrix criteria for the Lyapunov order