How to characterize commutativity equalities for Drazin inverses of matrices

Y. Tian

Address.
Department of Mathematics and Statistics, Queen's University,
Kingston, Ontario, Canada K7L 3N6.

E-mail: ytian@mast.queensu.ca

Abstract.
Necessary and sufficient conditions are presented for the commutativity equalities
$A^*A^D = A^DA^*$, $A^{\dag}A^D = A^DA^{\dag}$, $A^{\dag}AA^D =
A^DAA^{\dag}$, $AA^DA^* = A^*A^DA$ and so on to hold by using rank
equalities of matrices. Some related topics are also examined.

AMSclassification. 15A03, 15A09, 15A27.

Keywords. Commutativity, Drazin inverse, Moore-Penrose inverse, rank equality, matrix expression.