Schur’s theorem and the Drazin inverse

Robert E. Hartwig

Vol. 78 (1978), No. 1, 133–138

DOI: 10.2140/pjm.1978.78.133

Abstract

It is shown that if M = is a square 2n × 2n matrix over a ring R, such that AC = CA ∈ R_n×n, and with the property that A and C possess Drazin inverses, then M is invertible in R_2n×2n if and only if DA-BC is invertible in R_n×n.

Mathematical Subject Classification 2000

Primary: 15A09

Milestones

Received: 2 June 1977

Revised: 7 December 1977

Published: 1 September 1978