Stability of acyclic matrices
The nondirect graph G(A) of an \(n\times n\)-matrix A is defined as a set of vertices \(\{\) 1,2,...,n\(\}\) and (i,j) is an edge of G(A) iff \(a_{ij}\neq 0\) or \(a_{ji}\neq 0\) (i\(\neq j)\). A matrix is called acyclic if its nondirected graph contains no cycles. The author finds necessary and sufficient conditions for an acyclic matrix A whose principal minors are nonnegative to be stable. The conditions are expressed in terms of G(A). Some conditions related to additive D-stable acyclic matrices are also given (A is called additive D-stable if \(D+\) is stable for every nonnegative diagonal matrix D).
scientific article; zbMATH DE number 3944043