46 E.Chakurov, R.Chakurova

Abstract. This paper considers irreducible matrices with a slightly dominant principal diagonal. The theorem of O.Taussky giving a sufficient condition for non–singularity of such matrices is generalized. A new sufficient condition for convergence of Jackoby’s method for solving systems of linear equations for which the matrix of coefficients has a slightly dominant principal diagonal is proved. Theorem of O.Taussky [1]. Let matrix D of n-th order satisfy the following conditions: (i) D is irreducible; (ii) D has a slightly dominant principal diagonal, i.e. Hi = |dii | − n∑ j=1 j 6=i |dij | ≥ 0, i = 1,..., n; (iii) There is a strict inequality at least for one i in above inequalities, i.e. there exists i0, 1 ≤ i0 ≤ n, for which Hi> 0. Then the matrix D is non-singular. Corollary. Let A = {aij} be an irreducible matrix for which the following conditions are satisfied: a) aii = 0, i = 1,..., n; b) n∑ j=1 j 6=i |aij | ≤ 1, c) There exists i0, for which n∑ j=1 j 6=i