A triangular matrix of the form
can be tested to determine if it is lower triangular in the Wolfram
Language using LowerTriangularMatrixQ[m].
A strictly lower triangular matrix is a lower triangular matrix having 0s along the diagonal
as well, i.e.,
More things to try:
Weisstein, Eric W. "Lower Triangular Matrix."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LowerTriangularMatrix.html