Types of Matrices:

There are different types of matrices like rectangular matrix, null matrix, square matrix, diagonal matrix etc. This post covers overview of different types of matrices.

**(1) Row Matrix:** Row matrix is a type of matrix which has just one row. It can have multiple columns but there is just a single row present in a row matrix. Example of row matrix can be given as

which has just one row but has three columns.

We can mathematically define row matrix as:

Matrix of the form where 1 represents just a single row and n represents number of columns.

**(2) Column Matrix: **Column matrix is a type of matrix which has just one column. It can have multiple rows but there is just one column present in a column matrix. Example of column matrix can be given as:

which has just one column but has three rows.

We can mathematically define column matrix as:

Matrix of the form where m represents number of rows and 1 represents just a single column.

**(3) Null Matrix: **Null matrix is a type of matrix which has all elements equal to zero. Example of null matrix can be given as . We can also mathematically define null matrix as**:**

where for all i,j.

**(4) Rectangular Matrix: **Rectangular matrix is a type of matrix which has unequal number of rows and columns. Example of rectangular matrix can be given as

, where we have unequal number of rows and columns in a matrix. Number of columns is 2 and number of rows is 3.

We can mathematically define rectangular matrix as matrix of the form where .

**(5) Square Matrix: Square Matrix **is a type of** matrix **which has equal number of** rows **and** columns. **Example of square matrix can be given as

, where we have equal number of rows and columns equal to 3.

We can define square matrix mathematically as matrix of the form where .

**(6) Diagonal Matrix: **It is type of square matrix which has all the non-diagonal elements equal to zero. For example, matrix is a diagonal matrix.

We can mathematically define diagonal matrix as a matrix of the form , where when .

**(7) Identity Matrix: **It is a type of square matrix which has all the main diagonal elements equal to 1 and all the non-diagonal elements equal to 0. It is also called unit matrix.

Example of unit matrix can be given as

We can mathematically define identity matrix as a matrix of the form , where

for and for .

**(8) Scalar Matrix: **It is a square matrix in which all the elements except those on the leading diagonal are zeros. For example, is an example of scalar matrix.

We can mathematically define scalar matrix as matrix of the form: , where

for and for , where k is any scalar.

**(9) Upper Triangular Matrix: **It is a type of square matrix whose all elements below main diagonal are equal to 0. For example, is an example of upper triangular matrix.

We can mathematically define upper triangular matrix as matrix of the form:

where for i>j.

**(10) Lower Triangular Matrix: **It is a type of square matrix whose all elements above main diagonal are equal to 0. For example. is an example of lower triangular matrix.

We can mathematically define lower triangular matrix as matrix of the form:

where for j>i.