How to characterize commutativity equalities for Drazin inverses of matrices

Y. Tian

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


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.