Pseudo-Schur complements and their properties

Authors:
M. Redivo-Zaglia
Affiliations:
Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via G.B. Belzoni 7, 35131 Padova, Italy
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

The notion of Schur complement of a partitioned matrix with a square nonsingular block is well known and it has many applications in various branches of mathematics. When the block is rectangular or singular, pseudo-Schur complements can be defined and studied. In particular, they satisfy an extension of the quotient property for Schur complements. A new proof of this property is given in this paper and various related topics are discussed.