arXiv subjects

Kavita Bisht

Publications and source records attributed to Kavita Bisht.

3 recordsLinked to original sources

arXiv2016

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

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.

math.RA↗

arXiv2016

Pseudo Principal Pivot Transform: The Group Inverse Case

In this short note, we prove a formula for the group inverse of a block matrix and consider the pseudo principal pivot transform expressed in terms of group inverses. Extensions of the usual principal pivot transform, where the usual inverse is replaced by the Moore-Penrose inverse, were considered in the literature. The objective here is to derive the corresponding formulae for the group generalized inverse. These are expected to be useful in our future work.

math.RA↗

arXiv2015

Pseudo Schur Complements, Pseudo Principal Pivot Transforms and Their Inheritance Properties

In this short note, we prove some basic results on pseudo Schur complement and the pseudo principal pivot transform of a block matrix. Pseudo Schur complement and pseudo principal pivot ransform are extensions of the Schur complement and the principal pivot transform, respectively, where the usual inverse is replaced by the Moore-Penrose inverse. The objective is to record these results for use in future.

math.FA↗