Vol. 78, No. 1, 1978

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Schur’s theorem and the Drazin inverse

Robert E. Hartwig

Vol. 78 (1978), No. 1, 133–138
Abstract

It is shown that if M = [     ]
A   C
B   D is a square 2n × 2n matrix over a ring R, such that AC = CA Rn×n, and with the property that A and C possess Drazin inverses, then M is invertible in R2n×2n if and only if DA-BC is invertible in Rn×n.

Mathematical Subject Classification 2000
Primary: 15A09
Milestones
Received: 2 June 1977
Revised: 7 December 1977
Published: 1 September 1978
Authors
Robert E. Hartwig