Horizontal Matrix

A matrix is an arrangement of complex and real numbers enclosed in brackets and arranged in the form of columns and rows. The matrix, which is a mathematical concept, has its properties. Based on these properties, the matrices are divided into various types. The order of a matrix is the number of rows, and the columns of a matrix are a property of a matrix. Based on this property, the matrices are divided into types such as a rectangular matrix, horizontal matrix, vertical matrix, etc. A horizontal matrix is a matrix in which the number of columns exceeds the number of rows.

The order of a matrix

is a rectangular arrangement in terms of columns and rows. So, any given matrix will have a specific number of rows and columns. The order of a matrix is the property of a matrix which represents the number of rows and the number of columns present in a particular matrix. 

The letters m and n are used in the form m×n to represent the order of a matrix. The m represents the number of rows in a matrix, and the n represents the number of columns in the matrix. The multiplication of m with n will give us the total number of elements present in a matrix.

The classification of matrices is based on the number of rows and columns.

Following are the types of matrices based on the number of rows and the columns contained by a matrix.

• Singleton matrix-

A singleton matrix is a matrix that contains only one row and only one column as it contains only one element.

• Square matrix-

 A square matrix is a type of matrix in which the number of rows of a matrix is equal to the number of columns present in a matrix.

• Rectangular matrix-

 In a rectangular matrix, the number of rows present in a matrix is not equal to the number of columns present in a matrix.

• Vertical matrix-

The number of rows in the vertical matrix is greater than the number of columns.

• Horizontal matrix-

The number of columns in the horizontal matrix is greater than the number of rows.

Let us study in-depth about the horizontal matrix.

The Horizontal matrix

A matrix of order m×n, in which the value of n is greater than the value of m. The letter m represents the number of rows in a matrix, and n represents the number of columns present in a matrix.

Hence, the definition of matrix states that in a horizontal matrix, the number of columns is always more than the number of rows.

As a greater number of columns are added to any matrix, the matrix continues to expand horizontally. Hence, the shape of a matrix is more spread in the horizontal direction than in the vertical; hence such matrices are called the horizontal matrices. The horizontal entries in a matrix are more than the vertical entries.

A horizontal matrix example is:

The above matrix contains 2 rows and 3 columns. Hence it fulfils the condition of being a horizontal matrix. As you can see in the above diagram, the matrix is more expanded in the horizontal direction than in the vertical direction.

Let’s study the properties of a horizontal matrix.

Properties of a horizontal matrix

The following are the properties of a horizontal matrix.

• The most important property of a horizontal matrix is that the number of columns in a horizontal matrix is more than the number of rows.

• The order of a horizontal matrix is m×n with the condition that the value should always be less than the value of n.

• A horizontal matrix is always a rectangular matrix. Since the number of columns needs to be more in a horizontal matrix than the number of rows, a horizontal cannot be a square matrix and is a rectangular matrix.

• The transpose of a horizontal matrix will become a vertical matrix. That means the number of rows will now be switched with the number of columns. Hence the number of rows will exceed the number of columns.

A horizontal matrix could never be a symmetric matrix since the number of columns is not equal to the number of rows in a horizontal matrix. Hence, the transpose of the horizontal matrix will not be identical to the horizontal matrix itself.

Conclusion:

The number of rows and columns present in a matrix helps determine the shape, size and type of a matrix. The matrices that contain more columns than the number of rows appear horizontal in shape and are called horizontal matrices. The horizontal matrices are a type of rectangular matrix. All the row matrices are horizontal. The order of a horizontal matrix is m×n, where the value of n should always exceed the value of m. The transpose of a horizontal matrix is a vertical matrix.