ELA, Volume 4, pp. 39-47, October 1998, abstract.

P^alpha-matrices and Lyapunov scalar stability

Daniel Hershkowitz and Nira Mashal


For partitions alpha of {1,...,n}, the classes of P^alpha-matrices are defined, 
unifying the classes of the real P-matrices and of the real positive definite 
matrices. Lyapunov scalar stability of matrices is defined and characterized, 
and it is shown also that every real Lyapunov alpha-scalar stable matrix is a
P^alpha-matrix. Implication relations between Lyapunov scalar stability and 
H-stability are discussed.