Where rank is the number of linearly independent rows in a matrix.

In other words, a basis is a linearly independent spanning set.

Thus may be considered as a linearly independent basis for .

Thus is the second linearly independent solution we were looking for.

However, this solution lacks linearly independent solutions from the other roots.

It directly measures the number of linearly independent paths through a program's source code.

In more general terms, a basis is a linearly independent spanning set.

This can be done if and only if S is linearly independent.

From 2., are linearly independent, and the dimension of is .

In some cases, there will be two linearly independent solutions of that form.