Here you will learn what is the scalar matrix definition and order of scalar matrix with examples.
Let’s begin –
Scalar Matrix
Definition : A square matrix A = \([a_{ij}]_{n\times n}\) is called a scalar matrix if
(i) \(a_{ij}\) = 0 for all i \(\ne\) j and,
(ii) \(a_{ii}\) = c, for all i, where c \(\ne\) 0
In other words, a diagonal matrix in which all the diagonal elements are equal is called the scalar matrix.
Also Read : Different Types of Matrices – Definitions and Examples
Examples :
1). \(\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}\) is a scalar matrix.
The order of above matrix is \(3 \times 3\).
2). \(\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}\) is a scalar matrix.
The order of above matrix is \(2 \times 2\)
3). \(\begin{bmatrix} 3 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end{bmatrix}\) is a scalar matrix.
The order of above matrix is \(4 \times 4\).
