Here you will learn what is the square matrix definition and order of square matrix with examples.
Let’s begin –
Square Matrix
Definition : A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n.
A square matrix of order n is also called a n-rowed square matrix. The element \(a_{ij}\) of a square matrix A = \([a_{ij}]_{n\times n}\) for which i = j i.e. the elements \(a_{11}\), \(a_{22}\), …. , \(a_{nn}\) are called the diagonal elements and the line along which they lie is called the principal diagonal or leading diagonal of the matrix.
The order of a square matrix is \(n \times n\).
The general form of square matrix is \(\begin{bmatrix}a_{11} & a_{12} & …… & a_{1n} \\ a_{21} & a_{22} & …… & a_{2n}\\ . & . & . \\ a_{n1} & a_{n2} & …… & a_{nn} \end{bmatrix}\)
Also Read : Different Types of Matrices – Definitions and Examples
Examples :
1). \(\begin{bmatrix} 2 & 1 & -1 \\ 3 & -2 & 5 \\ 1 & 5 & -3 \end{bmatrix}\) is a square matrix.
The order of above matrix is \(3 \times 3\) and diagonal elements are 2, -2 and -3.
2). \(\begin{bmatrix} 2 & 1 \\ 3 & -2 \end{bmatrix}\) is a square matrix.
The order of above matrix is \(2 \times 2\) and diagonal elements are 2, -2.
3). \(\begin{bmatrix} 2 & 1 & -1 & 4 \\ 3 & -2 & 5 & 1 \\ 1 & 5 & -3 & 2 \\ 4 & 5 & 7 & 9 \end{bmatrix}\) is a square matrix.
The order of above matrix is \(4 \times 4\) and diagonal elements are 2, -2, -3 and 9.
