(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Well all the usual definition of exterior algebras, and tensor products are needed.

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Wedge product question

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