Vanishing Pseudo Schur Complements, Reverse Order Laws, Absorption Laws and Inheritance Properties

2016/11/16 by Kavita Bisht, Bisht, Kavita, K. C. ‎Sivakumar +1
Computer Science · Materials Science · Mathematics · #15A09 #15A24 #Advanced Optimization Algorithms Research #FOS: Mathematics #Liquid Crystal Research Advancements #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1611.05442

openalex publication_date 2016/11/16 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28

Abstract

The problem of when the vanishing of a (generalized) Schur complement of a block matrix (corresponding to the leading principal subblock) implies that the other (generalized) Schur complement (corresponding to the trailing principal subblock) is zero, is revisited. A simple proof is presented. Absorption laws for two important classes of generalized inverses are considered next. Inheritance properties of the generalized Schur compements in relation to the absorption laws are derived. Inheritance by the generalized principal pivot transform is also studied.

Related

• Pseudo Schur Complements, Pseudo Principal Pivot Transforms and Their Inheritance Properties
• Generalized Principal Pivot Transform and its Inheritance Properties
• On the existence of group inverses of Peirce corner matrices
• Schur Multipliers and Matrix Products
• Representations for the Drazin inverse of the generalized Schur complement