Column Matrix

Not the matrix, but a specific number associated with a square array of numbers known as the determinant, was the first to be recognised. The concept of the matrix as an algebraic entity emerged gradually. The term matrix was coined in the nineteenth century by the English mathematician James Sylvester, but it was his friend, the mathematician Arthur Cayley, who developed the algebraic aspect of matrices in two papers published in the 1850s. Cayley first used them to study systems of linear equations, and they are still very useful today.

A column matrix is a matrix with all of its elements contained within a single column. A column matrix’s elements are arranged vertically, and its order is n x 1. A column matrix has one column and many rows, the number of which is equal to the number of elements in the column.

MATRIX:-

Matrix is the plural form of matrix, which is a rectangular array or table containing numbers or elements arranged in rows and columns. They can have as many columns and rows as they want. Addition, scalar multiplication, multiplication, transposition, and other operations can be performed on matrices.

There are some rules to follow when performing these matrix operations, such as they can only be added or subtracted if they have the same number of rows and columns, and they can only be multiplied if the columns in the first and rows in the second are exactly the same. 

WHAT IS COLUMN MATRIX?

A column matrix is a matrix in which all of the elements are contained within a single The matrices listed below are excellent examples of column matrices . One column and several rows make up a column matrix. A column matrix has n elements and an order of n x 1. The elements are vertically arranged, with the number of elements equal to the number of rows in a column matrix. 

COLUMN MATRIX CHARACTERISTICS:-

The following column matrix properties aid in a better understanding of the column matrix:-

• In a column matrix, there is only one column.
• A column matrix has many rows.
• The number of elements in a column matrix is equal to the matrix’s row count.
• A rectangular matrix is also a column matrix.
• A column matrix’s transpose is a row matrix.
• Only a column matrix of the same order can be added or subtracted from.
• Only a row matrix can be multiplied by a column matrix.
• A singleton matrix is obtained by multiplying a column matrix by a row matrix.

EXAMPLES:- 

The matrices listed below are excellent examples of column matrices:-

A=[7]  

A is a column matrix with the dimensions 1x 1. Only one element is displayed in each row and column of this column matrix.

OPERATING ON COLUMN MATRIX:-

Across column matrices, the algebraic operations of addition, subtraction, multiplication, and division can be done. Column matrices can have the same addition and subtraction operations as other matrices. Only another column matrix can be added to or subtracted from a column matrix. The two matrices should be in the same order here.

The multiplication of a column matrix by a row matrix is conceivable. To satisfy the matrix multiplication criterion, the number of columns in the first matrix must equal the number of rows in the second matrix. That is, the number of rows in the row column is equal to the number of columns in the column matrix for multiplication.

When a column matrix is multiplied by a row matrix, the output is a square matrix. Furthermore, because the inverse of a column matrix does not exist, the column matrix cannot be utilised for division.

CONCLUSION:-

A column matrix is a matrix with only one column.The column matrix’s order is represented by m x 1, therefore each row will contain a single element arranged in such a way that it represents a column. In a matrix, the elements are stored in rows and columns. The row elements are organised horizontally, whereas the column elements are positioned vertically.

A column matrix’s determinant can only be found if its order is 1 x 1. The determinant is unknown if the matrix’s order is m x 1, where m is bigger than 1. As a result, only square matrices have determinants. A column matrix is one in which all of the elements are contained within a single column. There is only one column and several rows in a column matrix. A column matrix has n items and has an order of n 1. The items are organised vertically in a column matrix, with the number of elements equal to the number of rows.