Matrices over residuated lattices

Residuated lattices simultaneously generalise lattice-ordered groups and the structures used to model various many-valued logics (e.g., Boolean algebras, Heyting algebras and MV-algebras). Matrices over residuated lattices are of interest in data analysis (specifically formal concept analysis) and tropical mathematics, and the linear algebra of such matrices can be surprisingly similar to that of matrices over a field. I will describe some of the ways in which linear algebra over residuated lattices is like—and is unlike—linear algebra over fields