Range

For a matrix , the range of denoted as is defined as . This represents all vectors in that can be written as a linear combination of the columns of . It is also called the column space or image of denoted or .

Example

Go to Basis and Dimension of Range to see a worked example of finding the basis and dimension of a range.

If such that , then all the columns of that contains a Pivot form a basis of .

If such that with then the first columns of form a basis of .