Relationships between different sets involving group and Drazin projectors and nonnegativity

This paper deals with nonnegativity of matrices and their group or Drazin inverses. Firstly, the nonnegativity of a square matrix A, its group inverse A# and its group projector AA# is used to define different sets for which relationships and characterizations are given. Next, an extension of the previous results for index greater than 1 is presented. Similar sets are introduced and studied for Drazin inverses and Drazin projectors considering the core-nilpotent decomposition. In addition, the results are applied to study the {l}-Drazin periodic matrices for l⩾1.