Geodesic
How to characterize commutativity equalities for Drazin inverses of matrices
Archivum mathematicum, Tome 39 (2003) no. 3, pp. 191-199

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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.
Classification : 15A03, 15A09, 15A27
Keywords: commutativity; Drazin inverse; Moore-Penrose inverse; rank equality; matrix expression 
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     author = {Tian, Yongge},
     title = {How to characterize commutativity equalities for {Drazin} inverses of matrices},
     journal = {Archivum mathematicum},
     pages = {191--199},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {2003},
     mrnumber = {2010720},
     zbl = {1122.15300},
     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/