Criteria for the nonsingularity of partitioned matrices

摘要

From the applicational point of view, the most interesting criteria for the nonsingularity of a matrix are those which use the moduli of the elements and their simple combinations only. Some criteria of this type have been found by Pupkov, who generalized the Theorem of Hadamard and a result of Ostrowski. This paper generalizes the Pupkov criteria to the case of the partitioned matrices and presents some applications of the obtained results. Moreover, the paper generalizes some results of Pearce and Okuguchi concerning the matrices with dominating diagonal blocks.