Block representations of generalized inverses of matrices

TL;DR

This paper explores block representations of various generalized inverses of matrices, including Moore-Penrose and group inverses, using Rhode's technique and providing calculation methods with examples.

Contribution

It introduces block form representations for different types of generalized inverses and applies Rhode's technique to derive and compute these inverses.

Findings

Block representations for {1, 2, 3, 4, 5, 5^k}-inverses are established.

Methods for calculating generalized inverses are demonstrated with examples.

The paper extends existing techniques to new inverse forms.

Abstract

In this paper will be considered standard forms of generalized inverses for matrices in the shape of block representations {1, 2, 3, 4, 5, 5^k}-inverse. Especially will be considered Moore-Penrose inverse and the group inverse. Results from Rhode's technique are used and methods for calculating some inverse are shown on examples.