Diagonal Matrix – Definition and Examples

Here you will learn what is the diagonal matrix definition and order of diagonal matrix with examples.

Let’s begin –

Diagonal Matrix

Definition : A square matrix A = \([a_{ij}]_{n\times n}\) is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero

i.e. \(a_{ij}\) = 0  for all i \(\ne\) j.

A diagonal matrix of order \(n \times n\) having \(d_1\), \(d_2\), …. , \(d_n\) as diagonal elements is denoted by \(diag[d_1, d_2, …. , d_n]\).

Also Read : Different Types of Matrices – Definitions and Examples

Examples :

1). \(\begin{bmatrix} 1 & 0 & 0 \\ 0 &  2 & 0 \\ 0 & 0 &  3  \end{bmatrix}\) is a diagonal matrix.

The order of above matrix is \(3 \times 3\) and it is denoted by diag[1, 2, 3].

2). \(\begin{bmatrix} 2 & 0 \\ 0 &  -2 \end{bmatrix}\) is a diagonal matrix.

The order of above matrix is \(2 \times 2\) and it is denoted by diag[2, -2].

3). \(\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 &  2 & 0 & 0 \\ 0 & 0 &  3 & 0 \\ 0 & 0 & 0 & 4  \end{bmatrix}\) is a diagonal matrix.

The order of above matrix is \(4 \times 4\) and it is denoted by diag[1, 2, 3, 4].

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