Matrix is demonstrated as a set of numbers arranged in columns and rows. The numeric values written in the matrix are called the elements of the matrix. All mathematical computations are done with these elements to obtain the results. The study to define matrix and their types is very simple. Although, the best thing about the matrix study is that all types of operations, whether addition or division, are applicable. However, the way of solving these operations is simple and different in different types of matrix. 

Matrix 

Let’s define matrices and their types with this article. 

Matrix is demonstrated as a set of numbers arranged sequentially in a row and columns. In simple words, the matrix is defined as a rectangular array where all the elements are systematically arranged in columns and rows. Any matrix is mainly called by its order. So, the order of the matrix is defined as the number of rows and columns present in a given matrix. The rows and columns define the matrix and its types. 

Types of matrix

Let’s learn about the types of  matrices in detail. Here, we learn about the types of matrices with examples. 

There are twelve types of matrix. These are

• Column matrix 

• Row matrix 

• Square matrix 

• Null matrix 

• Diagonal matrix 

• Lower triangular matrix

• Upper triangular matrix 

• Skew -symmetric matrix

• Symmetric matrix 

• Vertical matrix 

• Horizontal matrix 

• Identity matrix 

Null matrix 

A null matrix is defined as a type of matrix whose all the elements are equal to zero. The matrix is also called a zero matrix and is usually demonstrated with a numeric value, 0. 

Example: If a matrix has two rows and two columns, then the total number of elements will become 4. So, all the four elements will be zero in a null matrix. 

Triangular matrix 

The triangular types are subdivided into two parts. These are:

• Lower triangular matrix 

• Upper triangular matrix 

Lower triangular matrix

The lower triangular matrix is a matrix that only contains numeric values in the lower element. In this matrix type, the elements written below the diagonal contain numeric values; otherwise, all the elements above the diagonal are zero. 

Upper triangular matrix 

The upper triangular matrix is a matrix that only contains numeric values in the upper element. In this matrix type, the elements written above the diagonal contain numeric values; otherwise, all the elements below the diagonal are zero. 

Vertical matrix 

A vertical matrix is defined as a matrix of order m×n, where m demonstrates the number of rows and the whole n demonstrates the number of columns. However, in a vertical matrix, the number of rows is greater than the number of columns. 

Horizontal matrix 

The horizontal matrix is similar to the vertical matrix. But the only difference is that in the vertical matrix, the number of rows is greater than the number of columns, while in the horizontal matrix, the number of columns is greater than the number of rows. 

Row matrix 

The row matrix only contains elements in the row. In the row matrix, the matrix column does not contain any type of numerical value. 

Column matrix 

The column matrix only contains elements in the column. In the column matrix, the row of the matrix does not contain any numerical value. 

Diagonal matrix 

In a diagonal matrix, the elements or entries in the diagonal only contain the numeric value. Otherwise, all the elements written below or above the diagonal contain zero value in this matrix type. 

Symmetric matrix 

The symmetric matrix is defined as a matrix whose mirror elements are similar. In a symmetric matrix, all the matrix diagonal elements are different. But the elements below or above the diagonal are equal; they form a mirror image of each other. 

Skew -Symmetric Matrix

The Skew -Symmetric Matrix is similar to the symmetric matrix, but the difference is that the sign of the elements on the opposite sides gets changed.

Identity matrix 

It is the special case of a matrix, in which all the elements in the diagonal are one, and the others are zero. 

So, this is how to define matrix and its types