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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