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

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.
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
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.
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:
Types of MatricesDifferent Types of Matrices
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 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.
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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 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.

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