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.

Also Read : Different Types of Matrices – Definitions and Examples

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 \(4 \times 4\).

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