A strictly upper triangular matrix is an upper triangular matrix having 0s along the diagonal as well as the lower portion, i.e., a matrix A = [a_(i j)] such that a_(i j) = 0 for i>=j. Written explicitly, U = [0 | a_12 | ... | a_(1n) 0 | 0 | ... | a_(2n) ⋮ | ⋮ | ⋱ | ⋮ 0 | 0 | ... | 0].

lower triangular matrix | strictly lower triangular matrix | triangular matrix