Lyapunov diagonal semistability of acyclic matrices
Daniel Hershkowitz · Linear and Multilinear Algebra · 1988
It is shown that an acyclic matrix is Lyapunov diagonally semistable if and only if the matrix has the weak principal submatrix rank property. This result completes the solution of the problem of characterizing the various types of matrix stability for acyclic matrices. Also, those acyclic matrices which have a unique Lyapunov scaling factor are characterized.