Generalized Pseudoskeleton Decompositions

TL;DR

This paper extends the theory of pseudoskeleton (CUR) decompositions to matrices and tensors over arbitrary fields, using generalized inverses instead of Moore--Penrose pseudoinverses, broadening their applicability.

Contribution

It provides new characterizations of pseudoskeleton decompositions applicable to any field and involving generalized inverses, unlike previous work limited to real or complex matrices.

Findings

Extended pseudoskeleton decompositions to arbitrary fields

Used generalized inverses instead of Moore--Penrose pseudoinverses

Broadened applicability to matrices and tensors over any field

Abstract

We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to arbitrary fields and to decompositions which use generalized inverses of the constituent matrices, in contrast to Moore--Penrose pseudoinverses in prior works which are specific to real or complex valued matrices, and are significantly more structured.