The representations of the Drazin inverse of differences of two matrices

In this paper, we give explicit representations of ( P ± Q) D , ( P ± PQ) D and ( PQ) # of two matrices P and Q, as a function of P, Q, P D and Q D , under the conditions P 3 Q = QP and Q 3 P = PQ.

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Veröffentlicht in:	Applied mathematics and computation 2010-08, Vol.216 (12), p.3652-3661
Hauptverfasser:	Liu, Xiaoji, Xu, Liang, Yu, Yaoming
Format:	Artikel
Sprache:	eng
Schlagworte:	Computation Drazin inverse Exact sciences and technology Group inverse Idempotent Inverse Mathematical analysis Mathematical models Mathematics Matrices Matrix methods Numerical analysis Numerical analysis. Scientific computation Quadratic programming Representations Sciences and techniques of general use
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Beschreibung
Zusammenfassung:	In this paper, we give explicit representations of ( P ± Q) D , ( P ± PQ) D and ( PQ) # of two matrices P and Q, as a function of P, Q, P D and Q D , under the conditions P 3 Q = QP and Q 3 P = PQ.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2010.05.016