Abstract
The aim of the paper is to explore non-local reverse-space matrix non-linear Schrodinger equations and their inverse scattering transforms. Riemann-Hilbert problems are formulated to analyse the inverse scattering problems, and the Sokhotski-Plemelj formula is used to determine Gelfand-Levitan-Marchenko-type integral equations for generalised matrix Jost solutions. Soliton solutions are constructed through the reflectionless transforms associated with poles of the Riemann-Hilbert problems.