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Let $W = \{ p(B) : p \text{ is a polynomial with real coefficients}\}$, where $$B= \begin{pmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 0 & 0 \end{pmatrix}$$

Which of the following possibilities presents the tightest bounds on the dimension $d$ of the vector space $W$?

  1. $4 ≤ d ≤ 6$
  2. $6 ≤ d ≤ 9$
  3. $3 ≤ d ≤ 8$
  4. $3 ≤ d ≤ 4$
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    Could you phrase your post as a question, and also tell us what you have tried so far?2012-12-19
  • 0
    I edited this post to turn it into a *question*. I may edit it further to provide some motivation and/or context.2015-06-03

3 Answers 3