Triangular Matrix

Definition

A square matrix in which all the entries above the main diagonal are zero is called lower triangular matrix.

A square matrix in which all the entries below the main diagonal are zero is called upper triangular matrix.

A matrix that is either upper triangular or lower triangular is called triangular matrix.

Example

$$\begin{array}{rl}\text{Upper Triangular Matrix}& :\left[\begin{array}{ccc}5& 2& 7\\ 0& 3& 1\\ 0& 0& 8\end{array}\right]\\ & \\ \text{Lower Triangular Matrix}& :\left[\begin{array}{ccc}4& 0& 0\\ 1& 6& 0\\ 3& 2& 9\end{array}\right]\end{array}$$