Tagged Questions
5
votes
1answer
151 views
Dimensions of vector spaces in an exact sequence
I've read the following formula in wikipedia:
Given finite dimensional vector spaces $V_i$ and an exact sequence
$\cdots\rightarrow V_i\rightarrow V_{i+1}\rightarrow\cdots$, we have
$$
\sum_{n\in ...
2
votes
1answer
364 views
When is the pullback of a linear injection a surjection on dual space?
Due to the contravariance of the dual space functor on vector spaces, one might expect the pullback of an injection to be a surjection, and the pullback of a surjection to be an injection. Indeed, for ...
3
votes
2answers
237 views
limits of finite dimensional vector spaces
Let $A$ be a finite dimensional vector space, $\cdots \rightarrow A_{n+1}\rightarrow^{f_{n+1}} A_n \rightarrow^{f_{n}} A_{n-1}\rightarrow \cdots $ be an inverse system of finite dimensional vector ...
