Geometry structures of the generalized inverses of block two-by-two matrices

Geometry structures of the generalized inverses of block two-by-two matrices

In this paper, we study the invertibility and the Moore–Penrose invertibility of 2×2 block matrix with Schur complement having closed range. The necessary and sufficient conditions for the existence as well as the expressions for the inverses and the Moore–Penrose inverses are obtained.

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Veröffentlicht in:Applied mathematics and computation 2015-01, Vol.250, p.479-491
1. Verfasser: Deng, Chunyuan
Format: Artikel
Sprache:eng
Schlagworte:
Block matrix
Blocking
Complement
Computation
Inverse
Mathematical analysis
Mathematical models
Matrices (mathematics)
Matrix methods
Moore–Penrose inverse
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Zusammenfassung:In this paper, we study the invertibility and the Moore–Penrose invertibility of 2×2 block matrix with Schur complement having closed range. The necessary and sufficient conditions for the existence as well as the expressions for the inverses and the Moore–Penrose inverses are obtained.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.11.008