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arXiv · 2608.23324

Least-Squares and Low-Rank Approximation for Linear Relations Using a Diagrammatic Language

Júlia de Araújo Mota·Iago Leal de Freitas·Lucas Rufino·João Paixão
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Abstract

We employ the machinery of linear relations to the study of optimization problems in linear algebra. We first show that the relational version of the pseudo-inverse can be realized through a generalization of the least-squares problem. This allows one to prove that the pseudo-inverse realizes the solution of certain relational optimization problems. Our main result is showing that a certain truncation of this pseudo-inverse defines a solution to a relational version of the classical low-rank approximation problem which recovers both the Eckart-Young Theorem and several optimization problems involving pairs of matrices and vector spaces.

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BibTeXRIS

Júlia de Araújo Mota, Iago Leal de Freitas, Lucas Rufino, João Paixão. 2026-08-24. Least-Squares and Low-Rank Approximation for Linear Relations Using a Diagrammatic Language. https://arxiv.org/abs/2608.23324

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