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Homework Statement
Please, I just am trying to understand the question. I wish to prove it on my own, but the way the question is phrased makes no sense.
So here it is:
Let us define the linear map
[tex]\phi : V^{*} \otimes \bigwedge^{i} V \rightarrow \bigwedge^{i-1} V[/tex]
by the formula
[tex]\ell \otimes v_1 \wedge ... \wedge v_i \mapsto \sum_{s=1}^{i} (-1)^{s-1} \ell (v_s) v_1 \wedge ... \wedge \hat{v_s} \wedge ... \wedge v_s [/tex]
Prove that the map [tex] \phi [/tex] is well defined and does not depend on the choice of basis.
Homework Equations
Well all the usual definition of exterior algebras, and tensor products are needed.
The Attempt at a Solution
As I stated, I haven't started solving yet, I am simply trying to understand the question. I don't see how it goes to wedge i-1. What exactly is v hat sub s? Does that make i wedges?
I don't think this formula is going to i-1 wedges. Please help me to understand what is going on here.