Types of matrices





In this page types of matrices we are going to see different types of matrix with detailed examples.

Row matrix

A matrix which is having only one row is called row matrix.

Examples:

 
5 -2 7 9
 
 
 
a b c
 
 

The order of first row matrix is 1 x 4

The order of second row matrix is 1 x 3


Column matrix

A matrix which is having only one column is called column matrix.

 
1
-2
0
 
 

The order of the above column matrix is 3 x 1

 
a
b
 
 

The order of the above column matrix is 2 x 1

Square matrix

A square matrix is a matrix in which the number of rows and the number of columns are equal. A matrix of order n x n is also known as a square matrix of order n.

In a square matrix A of the order n x n the elements a11,a22,a33........ann is called principal diagonal or leading diagonal or main diagonal elements.

 
3 2 1
-5 0 11
-3 2 8
 
 

The order of the above square matrix is 3 x 3.


Diagonal matrix

In a diagonal matrix all the entries except the entries along the main diagonal are zero.

 
4 0 0
0 5 0
0 0 6
 
 

Triangular matrix

A square matrix is known as a lower triangular matrix if all elements above main diagonal are zero .

 
3 2 1
0 5 3
0 0 1
 
 

A square matrix is known as a upper triangular matrix if all elements below main diagonal are zero .

 
3 0 0
5 8 0
1 -2 5
 
 

Scalar matrix

A square matrix is known as a scalar matrix if all the entries along the main diagonal are equal.

 
3 0
0 3
 
 

Identity (or) scalar matrix

When all the entries along the main diagonal are equal to 1 is known as identity matrix or unit matrix. Usually identity matrix is denoted by I₂ if the order of that particular matrix is 2 x 2 and it is denoted by I₃ if the order of that particular matrix is 3 x 3.

 
1 0
0 1
 
 


 
1 0 0
0 1 0
0 0 1
 
 

Zero matrix (or) null matrix (or) void matrix

In a matrix if all the entries are zero then it is called zero matrix.

 
0 0
0 0
 
 


 
0 0 0
0 0 0
0 0 0
 
 

Equality of matrices

Two matrices A and B are known as equality of matrices if both matrices is having same order. These are the types of matrices.


Transpose of matrix

A matrix formed by interchanging rows as columns and columns as rows is called as transpose of a matrix. The transpose of matrix A is usually denoted by A^T

If A =
 
1 5 7
     
2 3 8
 


then AT =
 
1   2
5   3
7   8
 
 
 







Types of Matrices to Matrix Introduction
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