Geodesic
How to characterize commutativity equalities for Drazin inverses of matrices
Archivum mathematicum, Tome 39 (2003) no. 3, pp. 191-199 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 15A03, 15A09, 15A27
Keywords: commutativity; Drazin inverse; Moore-Penrose inverse; rank equality; matrix expression 
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     volume = {39},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a4/}
}
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Tian, Yongge. How to characterize commutativity equalities for Drazin inverses of matrices. Archivum mathematicum, Tome 39 (2003) no. 3, pp. 191-199. http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a4/

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