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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

14 votes

Elementary $\mathrm{Ext}^1$ intuition

It seems like you already can see this, but $Ext^1(M,N)$ is measuring all the ways to form distinct short exact sequences $0\to N\to ?\to M\to 0$ If you are looking for intuition, what you should do i …
ArB's user avatar
  • 820
4 votes
Accepted

Matrices into path algebras

There's a slightly different equivalence that is also useful. Consider the quiver with n elements, and an arrow E_i from i to i+1 and another F_i from i+1 to i for all i. The relations are then that …
Kim Morrison's user avatar
  • 7,800