Strong Regularity of Matrices - A Survey of Results

Let Y = (G, @, I ) be a linearly ordered, commutative group and u@u = max(u, t’) for all u, IJEG. Extend 0, @ in the usual way on matrices over G. An m x n matrix A is said to have strongly linearly independent (SLI) columns, if for some b the system of equations A@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. We present also a similar theory developed for a structure based on a linearly ordered set where @ is maximum and @ is minimum.