# Lower Triangular Matrix – Definition and Examples

Here you will learn what is the lower triangular matrix definition with examples.

Let’s begin –

## Lower Triangular Matrix

Definition :

A square matrix A = $$[a_{ij}]$$ is called an lower triangular matrix if $$a_{ij}$$ = 0 for all  i < j.

Thus, in an lower triangular matrix, all elements above the main diagonal are zero.

## Examples :

1). $$\begin{bmatrix} 1 & 0 & 0 \\ 2 & 3 & 0 \\ 4 & 5 & 6 \end{bmatrix}$$ is a lower triangular matrix.

The order of above matrix is $$3 \times 3$$.

2). $$\begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}$$ is a lower triangular matrix.

The order of above matrix is $$2 \times 2$$.

3). $$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 2 & 3 & 0 & 0 \\ 4 & 5 & 6 & 0 \\ 7 & 8 & 9 & 5 \end{bmatrix}$$ is a lower triangular matrix.

The order of above matrix is $$4 \times 4$$.