Scalar Matrix – Definition and Examples

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 \(4 \times 4\).

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