Lesson plan
Cyclic vector
In the mathematics of operator theory, an operator A on an (infinite-dimensional) Banach space or Hilbert space H has a cyclic vector f if the vectors f, Af, A^2f,\dots span H . Equivalently, f is a cyclic vector for A in case the set of all vectors of the form p(A)f , where p varies over all polynomials, is dense in H .
Article summary
In the mathematics of operator theory, an operator A on an (infinite-dimensional) Banach space or Hilbert space H has a cyclic vector f if the vectors f, Af, A^2f,\dots span H . Equivalently, f is a cyclic vector for A in case the set of all vectors of the form p(A)f , where p varies over all polynomials, is dense in H .
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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