In Mathematics, there are different types of matrices. Some of them are as follows:

• Row Matrix
• Column Matrix
• Zero Matrix
• Square Matrix
• Diagonal Matrix
• Triangular Matrix
• Unit Matrix
• Symmetric Matrix
• Skew Symmetric Matrix

Row Matrix

A matrix which has one and only one row is called as a row matrix. A row matrix is of order 1xn.

Row Matrix Examples:

C = $\begin{bmatrix} 2 &-3 &6 &1 \end{bmatrix}$ is a matrix of order 1x4.

D = $\begin{bmatrix} 12 &13 &9 \end{bmatrix}$ is a matrix of order 1x3.

Column Matrix

A matrix which has one and only one column is called as a column matrix. A column matrix is of order mx1.

Column Matrix Examples

A = $\begin{bmatrix} 3\\ -6\\ 2\end{bmatrix}$ is a matrix of order 3x1.

B = $\begin{bmatrix} 37\\ 96\\ 7\\ 21\end{bmatrix}$ is a matrix of order 4x1

Zero Matrix

A matrix in which all the elements are zero is called as a Zero matrix. It is also called as Null matrix.

Zero Matrix Examples

$A_{2\times2}$ = $\begin{bmatrix} 0 &0 \\ 0 &0 \end{bmatrix}$ is a zero matrix of order 2x2.

$B_{3\times3}$ = $\begin{bmatrix} 0 &0 &0\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix}$ is a zero matrix of order 3x3.

Square Matrix

If the number of rows and number of columns of a matrix are equal, then the matrix is said to be a Square matrix. A = $\left [a_{i,j} \right ]_{m\times m }$ is a square matrix of order mxm.
The elements $a_{ij}$ of a square matrix for which i = j are called as Diagonal elements and the line along which they lie is said to be the Principal Diagonal of the given matrix. Let us look at few examples below:  In the above examples, 2, 8 are the diagonal elements of the matrix A and -1, 3, 1 are the diagonal elements of matrix B. The highlighted lines of matrices A and B are the Principal Diagonals.

Square Matrix Examples

$A_{2\times 2}$=$\begin{bmatrix} a &b \\ c &d \end{bmatrix}$ is a square matrix of order 2x2.

$B_{3 \times 3}$ =$\begin{bmatrix} b_{11} &b_{12} &b_{13} \\ b_{21} &b_{22} &b_{23} \\ b_{31} &b_{32} &b_{33} \end{bmatrix}$ is a square matrix of order 3x3.

$C_{4 \times4}$=$\begin{bmatrix} 1 &3 &-5 &7 \\ 2 &4 &6 &-8 \\ 3 &3 &9 &0 \\ 0 &3 &4 & 1 \end{bmatrix}$ is a matrix of order 4x4.

Diagonal Matrix

Diagonal matrix is a type of square matrix for which all the non diagonal elements are 0(zero). The matrix is denoted by diag(a, b, c) where a, b, c are the diagonal elements.

Diagonal Matrix Examples

D = $\begin{bmatrix} 6 &0 &0 \\ 0 &-9 &0 \\ 0 &0 &8 \end{bmatrix}$ is a diagonal matrix where 6, -9, 8 are the diagonal elements.

C = $\begin{bmatrix} 4 &0 \\ 0 &1 \end{bmatrix}$ is a diagonal matrix where 4, 1 are the diagonal elements.

Unit Matrix

If each of the diagonal elements of a square matrix is 1 and each non-diagonal elements is equal to zero, then this type of matrix is known as an unit matrix. In is the symbol of unit matrix, where n is the order of the given matrix.

Unit Matrix Examples

$I_{3\times 3}$= $\begin{bmatrix} 1 &0 &0 \\ 0 &1 &0 \\ 0 &0 &1 \end{bmatrix}$ is a unit matrix of order 3x3.

$I_{2\times 2}$= $\begin{bmatrix} 1 &0 \\ 0 &1 \end{bmatrix}$ is a unit matrix of order 2x2.

Symmetric and Skew-Symmetric Matrices

Symmetric Matrix: Symmetric matrix is a type of square matrix where its transpose is equal to the matrix itself. Let A be any square matrix and if A = AT, then $d_{i,j}$ =$d_{j,i}$

Symmetric Matrix Examples

$A_{3\times 3}$ = $\begin{bmatrix} b &g &h \\ g &c &e \\ h &e &a \end{bmatrix}$
In the above example, the transpose of matrix A is the same as that of A.

Skew-Symmetric Matrix:
Skew-symmetric matrix is a square matrix for which $d_{i,j}$ = -$d_{j,i}$, for all i and j.

Skew-Symmetric Matrix Examples

$A_{3\times 3}$ = $\begin{bmatrix} 0 &1 &2 \\ -1 &0 &3 \\ -2 &-3 &0 \end{bmatrix}$ is an example of skew-symmetric matrix.