Singleton Matrix

A matrix is a rectangular arrangement of numbers that can be real and complex in the form of columns and rows. These rows and columns are enclosed in brackets. The elements of a matrix are called the entry of a matrix. A matrix has an order which tells us the number of rows and the number of columns contained by that matrix. There are various types of matrices, such as the square matrix, a diagonal matrix, a unit matrix, singleton matrix, etc. A matrix that contains only one element is called a singleton matrix.

Definition and types of matrices

The arrangement of numbers that are real or complex in the form of rows and columns, which are enclosed in brackets, is called a matrix. 

There are various types of matrices, such as given below.

• Symmetric matrix:

An asymmetric matrix is a square Matrix in which the transport of the matrix is equal to the same matrix.

• Zero matrices:

A zero matrix is also called the null matrix, and all the entries in a zero matrix are equal to zero.

• Column matrix:

The Matrix, which contains only one column and any number of rows, is called a column matrix.

• Singleton matrix:

A matrix containing only one element is called a singleton matrix. Let us study in brief the singleton matrix.

Singleton matrix

As discussed above, a matrix in which only one element is present is called the singleton matrix. Following is an example of a singleton matrix.

[ 4 ]

Here, as we can see that the above matrix A contains only one element, that is 4. Hence it is a singleton matrix. 

The transpose of a singleton matrix A will be the same matrix as the rows and columns are switched while finding the transpose and rows and columns in the singleton matrix are similar.

Let’s take a look at what will be the order of a singleton matrix.

Order of a singleton matrix

The order of a matrix is a property of a matrix that represents the number of rows and the number of columns present in a matrix. The order of a matrix is the number of rows in a matrix × the number of columns in a matrix. The number of rows always comes first.

The order of a matrix is always represented in terms of m and n in the form m×n. Here m represents the number of rows in a matrix and represents the number of columns in a matrix. 

A singleton matrix contains only one element. Hence, only one row and only one column will be required to arrange the elements of a singleton matrix. 

So, the value of m, that is, the number of rows, will be equal to one, and the value of n, that is, the number of columns, will also be equal to one. Hence, the order of any singleton matrix is always equal to 1×1. 1×1 can also be regarded as the dimensions of the singleton matrix. Since the dimensions are in terms of 1, a singleton matrix is also called a singleton dimension matrix.

A singleton dimension matrix example is:

[ 7 ]

Let us take a look at the properties of a singleton matrix.

Properties of a singleton matrix

Following are the properties of a singleton matrix.

• The order of a singleton matrix is always equal to 1×1.

• A singleton matrix can only contain one element.

• A singleton matrix cannot contain any number of rows and any number of columns. The number of rows in the singleton matrix should always be equal to one, and the number of columns should also be one.

• Since the number of rows in a singleton matrix and the number of columns in a singleton matrix are both equal to 1, the singleton matrix is a square matrix.

• There is no restriction on what should be the entry in a singleton matrix, unlike in a zero matrix or unity matrix. Any number that is real or complex can be an entry in the singleton matrix.

• A singleton matrix can also be regarded as a row matrix as well as a column matrix: the number of rows in a singleton matrix is equal to one, and the number of columns in a singleton matrix is also equal to one.

Conclusion:

A singleton matrix is one of many types of matrices. A matrix is an arrangement of real and complex numbers in the form of rows and columns. These mattresses are classified based on their shape, the number of elements they contain, the type of elements they contain, etc. A singleton matrix is a type of matrix that contains only one element. This element can be any real or complex number. A singleton matrix is a square. The number of rows and number of columns in a singleton matrix are both equal to 1. Hence, the order of a singleton matrix is 1×1.