In mathematics, a shift matrix is a binary matrix with ones only on the superdiagonal or subdiagonal, and zeroes elsewhere. A shift matrix U with ones on the superdiagonal is an upper shift matrix.The alternative subdiagonal matrix L is unsurprisingly known as a lower shift matrix. The (i,j):th component of U and L are where is the Kronecker delta symbol. For example, the 5×5 shift matrices are Clearly, the transpose of a lower shift matrix is an upper shift matrix and vice versa.