Im new to linear algebra, so please just dont blast me.
If i have two linear spaces, with different names and equal dimensions. The two vector spaces are identical, apart from the name ?
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Yes, in the sense that if your spaces are $V$ and $W$, then there is a linear bijection from $V$ ont $W$, whose inverse is, of course, also a linear bijection. So, basically, yes, they are the same thing. More formally: even if $V\neq W$, $V$ and $W$ are isomorphic.