Linear Combination - Linear Independence

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

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