# On the Relative Gain Array (RGA) with Singular and Rectangular Matrices

arXiv: https://arxiv.org/abs/1805.10312 · HTML: https://mlsanity.com/paper/1805.10312/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2018.

## Built on by (most cited first, 1 of 1)

- [Tensor Completion with Provable Consistency and Fairness Guarantees for Recommender Systems](https://mlsanity.com/paper/2204.01815/) (2022)

## Abstract (arXiv)

In this paper we identify a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, we show that the conventional use of the Moore-Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. We then discuss how such properties can be rigorously preserved using an alternative generalized matrix inverse.