Definition:Triangular Matrix

Definition
Let $\mathbf T = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \\ \end{bmatrix}$ be a square matrix of order $n$.

Then $\mathbf T$ is a triangular matrix if all the elements either above or below the diagonal are zero.

Also see

 * Transpose of Upper Triangular Matrix is Lower Triangular