Clarity In Vertical Matrix

The use of matrices in algebra is to represent linear maps. The matrices are used in geometry to represent objects or their properties. Such matrices come in various shapes and sizes and are classified accordingly. The entries in matrices can be a real and complex number or some symbols and expressions. A vertical matrix is one of such various types of matrices. The number of rows in a vertical matrix exceeds the number of columns. This gives a matrix a vertical shape; hence it is known as the vertical matrix. Let’s study the in-depth vertical matrix.

Types of matrices based on the order

Any matrix represents the number of rows and the number of columns present in that matrix. The standard way of representing the order of a matrix is m×n, where m represents the number of rows and n represents the number of columns in a matrix.

The matrices are classified into various types based on their order. Following are those types of matrices.

• A square matrix

The square matrix is of the order n×n, which means the number of rows in a square matrix is equal to the number of columns in a square matrix.

• A rectangular matrix:

A rectangular matrix is of the order m×n, which means the number of rows in the rectangular matrix is not equal to the number of columns in a rectangular matrix.

• A horizontal matrix:

The horizontal matrix is of the order m×n with the condition that m×n. The number of rows in a horizontal matrix is smaller than the number of columns.

• A vertical matrix:

In a vertical matrix, the number of rows is greater than the number of columns.

Let us study in-depth about the vertical matrix and take a look at vertical matrix examples.

The vertical matrix

The matrix of the order m×n, with the condition that the value of m should be greater than n. The number of roses is represented by the letter m, and the letter n represents the number of columns.

Hence, as m>n, the number of rows in a vertical Matrix will be greater than the number of columns.

As more roses are added to a matrix, the matrix continues to grow vertically. Hence, the shape of the matrix spreads more in the vertical direction, and such a matrix is therefore named the vertical matrix. 

A vertical matrix example is given below.

The above matrix is of the order 3×2, which means the number of rows in this matrix is equal to 3, and the number of columns is equal to 2. As the number of rows exceeds the number of columns, the above matrix is vertical. You can observe in the above Matrix that the vertical shape of the above matrix is more than the horizontal shape. Let us study the properties of a vertical matrix.

Properties of a vertical matrix

Given below are a few properties of a vertical matrix.

•  The basic property of a vertical matrix is that the number of rows in the vertical matrix is more than the number of columns present.

• A vertical matrix will always be a rectangular matrix. As the condition for a vertical matrix is that the number of rows is greater than the number of columns, a horizontal matrix could never be a square matrix.

• The transpose of a vertical matrix is a horizontal matrix. While calculating the transports of a matrix, the number of rows is interchanged with the number of columns, the number of rows will decrease, and the number of columns will increase in the transposition of the matrix. Hence, the transpose will be a horizontal matrix.

• As the number of rows and the number of columns of a vertical matrix will always differ, a vertical matrix will not have properties like a determinant of diagonal elements.

A column matrix is a matrix that has only one column but can have multiple rows. Hence, the number of rows in a column matrix is always greater than the number of rows. So, a column matrix can be considered a vertical matrix.

These were a few properties of a vertical matrix.

Conclusion:

The matrices are simply an arrangement of numbers in symbols into rows and columns enclosed in a bracket. Matrices are classified into various types based on the number of these rows and columns, which is represented by order of the matrix. The vertical matrix is one such type of matrix. The number of rows in a vertical matrix is more than the number of columns. The column matrices are always vertical matrices. The transpose of a vertical matrix is a horizontal matrix. A vertical matrix is always a rectangular type of matrix.