Basis Vectors
A vector basis is a subset of vectors from V that can be used to generate any other element in V, using just additions and scalar multiplications.

A basis set, , is linearly dependent if:

Otherwise, the basis set is linearly independent.
A linearly independent basis set with i elements is said to span an i-dimensional vector space.

A basis set can be used to name or address a vector. This is the done by assigning the vector coordinates as follows:
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Lecture 9   Slide 4   6.837 Fall '00