# Types of matrices

Matrix theory is one of most important topic in mathematics , so it must be studied in detail to solve the mathematical problems with the help of matrix. One of the step in studying matrix is to study it’s types and example. Different types of matrices and it’s details are described below:

Note that it is possible for some matrices to belong in more than one type.

Types of matrices are as follows:
1> Row matrix:
A matrix having only one row is known as row matrix. for example:
, ,

2>Column matrix:
A matrix , having only one column is known as column matrix.
A matrix of order 2×1 is also called vector matrix.
For example:
, ,

3> square matrix:
A matrix having same number of rows and column is known as square matrix.
For example:
, and

4> Rectangular matrix:
A matrix that is not a square matrix or a matrix not having equal number of rows and column is known as rectangular matrix.
For example:
, and

5> Diagonal matrix:
A square matrix having all non-diagonal elements zero is known as diagonal matrix.
(NOTE: All the elements of square matrix whose row and column position is same are known as diagonal elements.)
For example:
, and

6> Scalar matrix:
A diagonal matrix having all the diagonal elements equal , is called scalar matrix.
For example:

7> unit matrix or Identity matrix:
A diagonal matrix having all the diagonal elements equal to 1 is known as unit or identity matrix.
For example:

8> Zero or null matrix:
Any matrix having all of its elements 0 is known as zero or null matrix.
For example:

9> Triangular matrix:
A square matrix having all the elements 0 either below the diagonal or above the diagonal is known as triangular matrix.

Note: A triangular matrix having elements 0 below diagonal is called upper triangular matrix ,A triangular matrix having elements 0 Above diagonal is called lower triangular

matrix and if a matrix have elements 0 both below and above the diagonal then it is a diagonal matrix.
For example:
,

10> Symmetric matrix:
A square matrix “A” is called a symmetric matrix if all of its elements follow the rule that : any element “a” is equal to another element whose row and column position is

equal to the column and row position of the element “a” respectively.
For example:

11> Skew-symmetric matrix:
A square matrix “A” is called a skew-symmetric matrix if all of its elements follow the rule that : any element “a” is equal to the negative value of another element whose

row and column position is equal to the column and row position of the element “a” respectively.
Note: Every skew-symmetric matrix have its diagonal elements 0.
For example:

12> Sub-matrix .
A matrix formed by eliminating some rows or columns or both of another matrix is called sub-matrix of the original matrix.
For example:
is a sub matrix of matrix

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