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.

Also Read : Different Types of Matrices – Definitions and Examples

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 \(4 \times 4\).

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