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].
