A note on Ostrowskiʼs Theorem

In this note, a further extension of Ostrowskiʼs Theorem, concerning mainly complex square irreducible matrices, is presented. Specifically, classes of irreducible matrices are determined for which the classical statement: “If for a matrix  A=[aij]∈Cn×nA=[aij]∈Cn×n,  n⩾2n⩾2, relations  |aii|>(∑j=1,j≠in|aij|)α(∑j=1,j≠in|aji|)1−αare satisfied for all  i∈{1,2,…,n}i∈{1,2,…,n}and for some  α∈[0,1]α∈[0,1], then, A is nonsingular”, can hold even if all the inequalities in it turn out to be equalities.