A band matrix is one for which elements far from the diagonal are zero; distance is usually required to be uniform in the sense that the remoteness of the farthest nonzero element must always be the same. That closer elements are zero does not materially affect the behavior of such a matrix, but deciding whether a border element is zero can be a delicate numerical problem. The band need not be centered, a configuration which would be an automatic consequence of its forming part of a symmetric matrix.