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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Replying to @ZachWeiner
Vector space includes the rules for adding and multiplying the vectors.
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Replying to @Noahpinion
I'm having trouble imagining what a set of vectors without rules is, but maybe this is somewhat semantic?
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Replying to @ZachWeiner @Noahpinion
For example, lets say you have a set of vectors V = {v1,v2}, if you do the sum: v3 = v1 + v2 It could be different from v1 and v2, this means V is not a vector space.
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Replying to @jelorias95 @ZachWeiner
Zach, what he means is that a vector space has to be "closed" under addition and multiplication. In other words, you can't add or multiply vectors in the space and get something that's not a vector in the space.
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Replying to @Noahpinion @ZachWeiner
Multiply by scalars, in general you don't have to be able to multiply vectors with vectors.
1 reply 0 retweets 1 like
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.
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