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__Basis__
for a vector space V is a set of vectors so that
any vector in V can be written as a unique linear
combination of these vectors.
__Ex. for the space (or more generally
)__
We always have a standard basis
where the
are:

This basis is a basis because for any
we have:
We will always use the standard basis (unless otherwise denoted).
Knowing what happens to a basis (vector) given that pattern for
what happens in every situation.

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Frederick Leitner
2004-05-12