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

Let V be a vector space of dimension n. And the linear operators E=A^0, A^1, A^2, ... A^(n-1) are linearly independent. Prove that there exists a v in V such that V=<v, Av, A^2v, ..., A^(n-1)v>

2. Relevant equations

3. The attempt at a solution

Here are something that I tried.

the degree of the minimal polynomials p(t) such that p(A)=0 is larger than n-1. I wanted to start the proof from here but have no idea how to proceed.

assume V is over complex field C so that there is an eigenvector. However, it seems that this is also not the disired v to make them independent.

Any hint? Thanks a lot

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# Homework Help: Vector space, basis, linear operator

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