Let 𝒢=(G,¸ª$,¸•) be a linearly ordered, commutative group and uℝpound;v=max(u,v) for all u,v∈G. Extend ¸ℝpound;,¸ª$ in the usual way on matrices over G. An m×n matrix A is said to have strongly linear independent (SLI) columns, if for some b the system of equations Aª$x=b has a unique solution. If, moreover, m=n then A is said to be strongly regular (SR). This paper is a survey of results concerning SLI and SR with emphasis on computational complexity. It presents also a similar theory developed for a structure based on a linearly ordered set where ¸ℝpound; is maximum and ¸ª$ is minimum.
