Perron Complements of Strictly Generalized Doubly Diagonally Dominant Matrices

Abstract

As \u00a0is \u00a0known, \u00a0Meyer \u00a0introduced \u00a0the \u00a0concept \u00a0of \u00a0the \u00a0Perron \u00a0complements \u00a0of \u00a0nonnegative irreducible matrices. In addition, the Schur complements of generalized doubly diagonally dominant matrices were \u00a0introduced \u00a0by \u00a0Liu \u00a0etal. \u00a0[Linear \u00a0Algebra \u00a0Appl., \u00a0378(2004): \u00a0231-244]. \u00a0In \u00a0this \u00a0paper, \u00a0properties \u00a0of \u00a0the Perron complement of strictly generalized doubly diagonally dominate matrices are presented.