Definition:Triangular Matrix/Lower Triangular Matrix

Definition
A lower triangular matrix is a square matrix in which all the elements above the diagonal are zero.

That is, all the non-zero elements are in the lower triangle:


 * $\mathbf L = \begin{bmatrix}

a_{11} & 0 & 0 & \cdots & 0 & 0 \\ a_{21} & a_{22} & 0 & \cdots & 0 & 0 \\ a_{31} & a_{32} & a_{33} & \cdots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ a_{n-1,1} & a_{n-1,2} & a_{n-1,3} & \cdots & a_{n-1,n-1} & 0 \\ a_{n1} & a_{n2} & a_{n3} & \cdots & a_{n-1,1} & a_{nn} \\ \end{bmatrix}$

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