This question might sound stupid to some of you, but i'm in the process of figuring out this whole coordinates subject.
Lets say V is an n dimensional vector space.
and lets say A and B are two different bases of V.
let v be vector in V.
now let be the coordinates vector of v with respect to A,
and let be the coordinates vector of v with respect to B.
now, my question is this:
geometrically speaking; are and the same vector? (i know that if n>3 then there's no geometric meaning to vectors, so let's say we're talking about 2 or 3 dimensional space)
and another one:
let's take for example .
what are its coordinates with respect to B?
thanks in advanced.