Vectors Represented in a Basis
Every vector has a unique representation in a given basis
- the multiples of the basis vectors are the vector’s components or coordinates
- changing the basis changes the components, but not the vector
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V = v1E1 + v2E2 + … vnEn
The vectors {E1, E2, …, En} are the basis
The scalars (v1, v2, …, vn) are the components of V with respect to the basis