A sufficient condition for matrix stability
Charles R. Johnson · Journal of Research of the National Bureau of Standards Section B Mathematical Sciences · 1974
An n by n comp lex matri x A is said to be pos itiv e stab le if Re ( A) > 0 for e ac h e ige nvalu e A of A.If A sati sfie s both of the followin g two conditions, th e n A is pos itiv e stable: (1) for eac h k = 1, .. ., n , th e real part of the sum of the k by k prin c ipal minors of A is pos itive ; and (2) the minimum of th e rea l parts of the e ige nvalues of A is it se lf an eigenvalu e of A. Special c ases in c lud e hermiti a n po sitive d e finite matri ces and M-matri ces.