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:
“In England the judges should have independence to protect the people against the crown. Here the judges should not be independent of the people, but be appointed for not more than seven years. The people would always re-elect the good judges.”
—Andrew Jackson (1767–1845)