RM was partially supported by Fondecyt-Concytec contract 100-2018 , HV was partially supported by Universidad Nacional de Ingeniería FC-PF-33-2021 and P-CC-2021-000666 . CAM was partially supported by CNPq -Brazil and the NRF Brain Pool Grant funded by the Korea government (No. 2020H1D3A2A01085417 ).

We extend the classical Banach-Mazur distance [3] from Banach spaces to linear operators between these spaces. We prove in the finite dimensional case that the corresponding topology is metrizable, complete, separable and locally compact. Furthermore, we prove that the Banach-Mazur compactum embeds isometrically into the resulting topological space. (C) 2020 Elsevier B.V. All rights reserved.