Usage of LU decomposition over UL decomposition What are some advantages of using LU decomposition over UL decomposition? From what I see, they can both be used equally well to solve $MX=V$ through forward and backward substitution, and since the determinant is commutative for triangular matricies, they can both be used. Some googling returns nothing on the UL decomposition, leading me to believe that LU has some advantages over UL. So why is LU decomposition preferred?

Source: Linear Algebra by Cherney, Denton, Waldron
In an otherwise banded matrix, sparseness is preserved by:
(1) LU decomposition when there are full rows at the bottom and/or
columns on the right;
(2) UL decomposition when there are full rows at the top and/or columns on
the left.
In an otherwise banded matrix, sparseness is preserved by:
(1) LU decomposition when there are full rows at the bottom and/or
columns on the right;
(2) UL decomposition when there are full rows at the top and/or columns on
the left.