The notion of Schur complement of a partitionedmatrix 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.
Pseudo-Schur complements and their properties
REDIVO ZAGLIA, MICHELA
2004
Abstract
The notion of Schur complement of a partitionedmatrix 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.
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10.1016-j.apnum.2004.05.004.pdf
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