Types of Matrices

Introduction

A matrix is the arrangement of numbers or digits or any other forms of mathematical expression like signs, symbols, etc in a rectangular formation that represents the properties of a specific mathematical dataset. These could be used in mathematics, computer language, and so on. In linear algebra, there are several types of matrices. The brief descriptions and explanations of each type of matrix are given below.

Body

Square Matrix:

In this matrix, the number of rows and columns should be equal and the matrix should look like a square. The matrix is mostly shown as (m X n) and both m and n are equal.

Symmetric Matrix

In this type of matrix, we can see a square matrix being equivalent to its transpose. 

Triangular Matrix

In this type of matrix, the digits or symbols over or under the primary diagonal are zero. This matrix can be divided into two groups, according to the location of the digits equal to zero. If digits over the principal diagonal are zero, then it is called the lower triangular matrix and when the digits below the principal diagonal are zero then it is called the upper triangular matrix.

Diagonal Matrix

In this type of matrix, the digits of the principal diagonal are not equivalent to zero, but the rest of them are equal to zero. This type of matrix may or may not be a square matrix.

Identity Matrix

This type of matrix is also known as a unit matrix. The matrix is square in shape and the digits from the principal diagonal can be seen as equivalent to 1 and the rest of the digits can be seen as equivalent to 0. When the matrix is multiplied its vectors remain unchanged.

Orthogonal Matrix

In this type of matrix, A.At is equivalent to I where A denotes the original matrix and I denote the identity version.

Row matrix

In this type of matrix, there should be only a single row. The number of columns is not of importance here, but the row should be only one. The row will be ordered in the equivalent form to 1 X n and n will signify the column number.

Column matrix

In this type of matrix, the number of columns should be only one. The number of rows is of no importance here and that can be one or more. But the column should be only one here. Here the matrix will be ordered as m X 1 in its column and m will denote the number of rows.

Rectangular matrix 

In this type of matrix, the number of rows and columns should not be equal and unlike square matrix, the numbers should be expressed with two different symbols. Usually, the matrix is denoted as (m X n) and here m signifies the number of rows and n signifies the number of columns in the matrix.

Vertical matrix 

In this type of matrix, the number of columns is less than the number of rows and the matrix looks like a standing column. The matrix is shown as (m X n) and m, which denotes the number of rows, is greater than n, which shows the number of columns.

Horizontal matrix

In this type of matrix, the number of columns is more than the number of rows and the matrix looks like a horizontal row. The matrix is shown as (m X n) and m, which denotes the number of rows, is less than n, which shows the number of columns.

Null matrix

This type of matrix is also called a zero matrix. In this matrix, all the elements should be zero. So the overall value of the matrix is null or zero.

Scalar matrix

The scalar matrix is similar to the functioning of the diagonal one in one aspect because, in this matrix, the digits over and under the primary diagonal have to be equivalent to zero. In this type of matrix, the digits from the principal diagonal must be equal.

Upper triangular matrix

In this type of matrix, the digits under the principal diagonal in a square matrix are equivalent to zero.

Lower triangular matrix

In this type of matrix, the digits over the principal diagonal in a square matrix are equivalent to zero.

Singular matrix

This type of matrix is square in shape and it possesses no inverse.

Idempotent matrix

In this type of matrix, matrix A is equivalent to A2.

Involutory matrix

In this type of matrix, A2 is seen as equal to I, where A denotes the matrix and I denote an identity matrix. This matrix is the inverse of the primary matrix or matrix A.

Anti-symmetric matrix

When a square matrix does not equal its transpose formation, then it is called an anti-symmetric matrix.

Transpose Matrix

In this type of matrix, the columns of a matrix have turned into rows and the rows of a matrix have been converted to columns. Thus one matrix is the transpose of the other one.

Conclusion

Thus the article has explained each type of matrix and has briefly identified different types of matrices used in business mathematics. They are an important part of linear algebra and they play a vital role in easing up difficult calculations and mathematics where multiple values are given. The identification of each type of matrix is very important for using the matrix with appropriate context and using those for solving mathematical problems without much effort.