Multidimensional physical quantities

Abstract In the present paper we present the continuation of the recent paper “One-dimensional physical quantities”, published in Revista Brasileira de Ensino de Física. The operational construction of a physical quantity passes through the definition of its domain, separation of the domain into equivalence classes and, finally, the injective association of equivalence classes into a value space. This formulation is outlined here to encompass multidimensional quantities, including vectors, dual vectors and tensors. Adopting an operational bias, in this case, allows us to re-signify seemingly tautological topics of mathematics, such as geometry and topology, from its connection to the physical world.