Vectors in a general vector space do not

**have** "components".

After you have defined a basis for the vector space,

**then** you can talk about "components". If, for example, your basis is

, then any vector, v, in that space can be written

. In that case, the "components of v" in

**this** basis, are the scalars

.

Any n dimensional vector space is

**isomophic** to

but it is wrong to say it "is"

. Exactly what that isomorphism is and how each vector would written in "components" depends, as I said before, on the choice of basis.