(Національний університет "Києво-Могилянська академія", 2025) Kravchuk, Oleg; Kriukova, Galyna
The Moore-Penrose pseudo-inverse is a foundational concept in modern numerical linear algebra, offering a principled approach to solving ill-posed and inconsistent systems arising in machine learning and other fields. This paper explores the pseudo-inverse from five distinct perspectives — axiomatic, variational, regularization, spectral, and algebraic graph theory — highlighting its theoretical depth and practical relevance across disciplines such as machine learning, signal processing, and network analysis.