Types of Matrices | Matrices

1. Zero (or null) Matrix:

A matrix having all elements equal to “zero” called zero matrix, i.e. $a_{ij}$ = 0.

Example:

A 3 x 3 zero matrix is $\begin{bmatrix}0 & 0 & 0\\
0 & 0 & 0\\
0 & 0 & 0
\end{bmatrix}$

2. Square Matrix:

A matrix with equal number of rows and columns is called square matrix.

Order of such matrix is n x n.

Example:

$\begin{bmatrix}1 & 2 & 3\\
4 & 5 & 6\\
7 & 8 & 9
\end{bmatrix}$ is a square matrix of order 3 x 3.

3. Diagonal Matrix:

A square matrix with all elements zero except diagonal elements, i.e. $a_{ij}$ = 0 for  i $\neq$ j.

In general, its form is

$A = \begin{bmatrix}a & 0 & … & 0\\
0 & a_{22} & … & 0\\
… & … & … & …\\
0 & 0 & … & a_{mn}
\end{bmatrix}$

4. Unit Matrix:

A diagonal matrix with all diagonal elements equal to “unit” (1) is called unit matrix.

Example:

A 3 x 3 unit matrix is written as $\begin{bmatrix}1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1
\end{bmatrix}$