"Abstract" linear algebra
This is more of a general question about whether we can do with Sage what we normally do as mathematicians on paper and in our minds. For example, if I do
V = VectorSpace(QQ,4)
W = VectorSpace(QQ,4)
I get: True. This is quite disturbing - while V and W are isomorphic they should not be identical. As I understand it, a vectorspace over QQ for Sage is just QQ^4, that's it. In other words, the Linear algebra package, while excellent, is not really about vector spaces but rather about arrays of numbers.
Any thoughts on this desire of mine to have a genuine "coordinate-free" approach?