Column Matrix
A column matrix is a type of matrix that has only one column and multiple rows. It is represented as:
where
Properties of a Column Matrix
1 Order of a Column Matrix
A column matrix is always of the order
Example
Consider a 4×1 column matrix:
Here, the matrix has 4 rows and 1 column, so its order is
2 Addition of Column Matrices
Two column matrices of the same order can be added by adding their corresponding elements.
Example
Let:
Then, the sum is:
3 Scalar Multiplication
A column matrix can be multiplied by a scalar (a single number) by multiplying each element by the scalar.
Example
Let:
Then, the scalar multiplication is:
4 Transpose of a Column Matrix
The transpose of a column matrix converts it into a row matrix.
Example
Let:
Then, its transpose is:
5 Multiplication of Two Column Matrices
Two column matrices cannot be directly multiplied unless one is transposed to form a row matrix.
Example
Let:
To perform matrix multiplication, we take the transpose of
The result is:
6 Identity Property
Multiplying a column matrix by an identity matrix of compatible order results in the original matrix.
Example
Let:
Then:
7 Zero Column Matrix
A column matrix in which all elements are zero is called a zero column matrix.
Example
For any column matrix