I'm not sure what you're after here but the inner product of two vectors in your vector space is a scalar and so cannot be "part of the vector space".

Have I missed your point?

Reply 5

DFranklin

Original post by ghostwalker

One reason is that you can have different inner products on the same vector space.

Another reason is that inner products only really make sense if the underlying field is

\mathbb{R}

\mathbb{C}

, but the idea of a vector space makes sense for any (non-trivial?) field.

Reply 6

ghostwalker

Original post by DFranklin

Another reason is that inner products only really make sense if the underlying field is

\mathbb{R}

\mathbb{C}

, but the idea of a vector space makes sense for any (non-trivial?) field.

I've noticed recently that I'm tending to miss the major cause, and pick up on minor one - must by old age.

Reply 7

DFranklin

Original post by ghostwalker

I've noticed recently that I'm tending to miss the major cause, and pick up on minor one - must by old age.

I'm not sure that this is any more "major" than your suggestion anyhow, but if it makes you feel better, it took a google search to find out that some vector spaces don't admit an inner product.