Abstract The concept of a uniformly linearly independent sequence, due to R.M. Elkin, is a useful notion. Convergence theory of iterative processes for solving nonlinear equations or optimization problems in R n is an example of a discipline which has benefited from the use of this notion. The purpose of this paper is to present some properties of a uniformly linearly independent sequence of subspaces of R n . The properties derived were motivated by convergence results of Elkin for “block univariate relaxation” methods.