Definition:Triangular Matrix

Definition
Let $\mathbf T = \begin {bmatrix} a_{1 1} & a_{1 2} & \cdots & a_{1 n} \\ a_{2 1} & a_{2 2} & \cdots & a_{2 n} \\ \vdots & \vdots & \ddots &  \vdots \\ a_{m 1} & a_{m 2} & \cdots & a_{m n} \\ \end {bmatrix}$ be a matrix of order $m \times n$.

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

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

Also see

 * Transpose of Upper Triangular Matrix is Lower Triangular