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- Thread starter asdf1
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http://www.math.niu.edu/~beachy/courses/240/vectorspace.html

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Hurkyl

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You don't because they don't.

To make a vector space, you need 3 things:

(1) A set of "vectors".

(2) A field of "scalars".

(3) An "addition" operation that takes two vectors and produces a vector.

(4) A "multiplication" operation that takes a scalar and a vector and produces a vector.

You've only specified (1), so that's certainly not enough to make a vector space. Once you specify the other three things, then we can start discussing the question of whether it's a vector space or not.

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