Аннотация:Abstract—Given a square nonnegative matrix A, a simple algorithm is suggested for constructinga stability indicator characterizing the localization of its spectrum in the unit disk. Theoremsare proved which establish the possibility to use the maximum of 1 − det(I − J) over all possibleprincipal submatrices J of A as a suitable indicator and give conditions under which such amaximum can be calculated only over a certain chain of leading principal submatrices. Appliedproblems that need such constructions and a relationship between the obtained results and similarresults established for a number of matrices of special form are considered.