Linear Independence
For some sets of vectors v1,...,vn, a single vector can be written in two different ways as a linear combination of them:
Equivalently, by subtracting these a non-trivial combination is zero:
If that is possible, then v1,...,vn are called linearly dependent; otherwise, they are linearly independent. Similarly, we can speak of linear dependence or independence of an arbitrary set S of vectors.
If S is linearly independent and the span of S equals V, then S is a basis for V.
Read more about this topic: Linear Combination
Famous quotes containing the word independence:
“To drive men from independence to live on alms, is itself great cruelty.”
—Edmund Burke (1729–1797)