For a matrix A, the tril(A) command returns a matrix R where R[i,j] = A[i,j] when R[i,j] is on or below the main diagonal of R. R[i,j] = 0, otherwise.

For a matrix A, the tril(A,k) command returns a matrix R where R[i,j] = A[i,j] when R[i,j] is on or below the diagonal of R indexed by k. R[i,j] = 0 otherwise.

The diagonals of a matrix are indexed using signed integers, where the main diagonal has index 0. Superdiagonals are indexed with positive integers and subdiagonals are indexed with negative integers.