Definition:Triangular Matrix/Lower Triangular Matrix

Definition
A lower triangular matrix is a matrix in which all the upper triangular elements are zero.

That is, all the non-zero elements are on the main diagonal or in the lower triangle.

That is, $\mathbf L$ is lower triangular :
 * $\forall a_{i j} \in \mathbf U: i < j \implies a_{i j} = 0$

Also defined as
Some sources define a lower triangular matrix only as a square matrix.

Also see

 * Definition:Lower Triangular Element


 * Definition:Upper Triangular Matrix