A square matrix in which every element lying to one side of the main diagonal is equal to zero. Thus for a lower triangular matrix, L,
and for an
upper triangular matrix,
U,
if, in addition,
then
L or
U is said to be
strictly lower or
strictly upper triangular respectively. The inverse of a lower (or an upper) triangular matrix, if it exists, is easy to calculate and is itself lower (or upper) triangular.