Band matrix: A matrix which has its non zero elements arranged uniformly near to the diagonal, so that aij = 0 if (i - j)> ml or (j - i)> mu where aij are the elements of matrix and ml and mu are the upper and lower band widths respectively and ml+mu+1 is the whole band width. The example of such a matrix is the below draw square matrix, A, with n number of rows, columns and band widths ml=q-1 and mu=p-1.

 

 These types of matrices often arise in numerical analysis. Diagonal, upper and lower triangular matrices are the special cases of the band matrices.