I'm going to teach myself some math, and I'll be asking lots of potentially stupid questions. First up: Is there a difference between saying "a vector space" and "a set of vectors" ?
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Multiply by scalars, in general you don't have to be able to multiply vectors with vectors.
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Right, if you can take the inner product between a vector and a vector, it's an inner product space, which is awesomer than just any ol' vector space.
End of conversation
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