# Column Matrix

## Definition

A matrix whose all elements are arranged in a column is called a Column matrix.

Column matrix is a type of matrix and it is also called as a column vector. All elements in this type of matrix are arranged in different rows but only in one column.

$M$ is a column matrix in general form and it is known as a column matrix of order $m \times 1$.

$M = {\begin{bmatrix} e_{11}\\ e_{21}\\ e_{31}\\ \vdots\\ e_{n1} \end{bmatrix}}_{\displaystyle m \times 1}$

The column matrix can be expressed in simple form.

$M = {\begin{bmatrix} e_{\displaystyle ij} \end{bmatrix}}_{\displaystyle m \times n}$

Each element in this matrix is arranged in a row but in only one column. Therefore, the column $j = 1$. Therefore, the number of columns is one. The general form column matrix can be expressed as follows.

$M = {\begin{bmatrix} e_{\displaystyle i1} \end{bmatrix}}_{\displaystyle m \times 1}$

### Example

Observe the following examples to understand how elements are arranged in column matrices.

$(1)\,\,\,\,$ $A = \begin{bmatrix} 7 \end{bmatrix}$

$A$ is a column matrix of order $1 \times 1$. In this column matrix, the only one element is displayed in one row and one column.

$(2)\,\,\,\,$ $B = \begin{bmatrix} -1\\ 4 \end{bmatrix}$

$B$ is a column matrix of order $2 \times 1$ and in this matrix, the two elements are arranged in two rows and one column.

$(3)\,\,\,\,$ $C = \begin{bmatrix} 6\\ 0\\ 9 \end{bmatrix}$

$C$ is a column matrix of order $3 \times 1$. The three elements are arranged in the matrix in three rows and one column.

$(4)\,\,\,\,$ $D = \begin{bmatrix} -5\\ 8\\ 2\\ 3 \end{bmatrix}$

$D$ is a column matrix of order $4 \times 1$. The four elements are arranged in the matrix in four rows and one column.

The column vector can have any number of elements but all the elements are arranged in number of rows but only in one column.

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