# Upper Triangular Matrix – Definition and Examples

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

Let’s begin –

## Upper Triangular Matrix

Definition :

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

Thus, in an upper triangular matrix, all elements below the main diagonal are zero.

## Examples :

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

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

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

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

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

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