Dashnic-Zusmanovich type matrices: A new subclass of nonsingular H-matrices

A new class of matrices, called Dashnic-Zusmanovich type (DZ-type) matrices, which is similar to, but different from Dashnic-Zusmanovich (DZ) matrices, is introduced and proved to be a subclass of nonsingular H-matrices. The relations between strictly diagonally dominant matrices, doubly strictly diagonally dominant matrices, DZ matrices and DZ-type matrices are discussed. Finally, by the non-singularity of DZ-type matrices, a new eigenvalue localization set for matrices is given.