I've been thinking about a problem I made up. The solution may be trivial or very difficult as I have not given too much thought to it, but I can't think of an answer of the top of my head.(adsbygoogle = window.adsbygoogle || []).push({});

Let ## T:V → V ## be a linear operator on a finite-dimensional vector space ##V##. Does there exist a vector ## v \in V ## for which the T-cyclic subspace of ##V## generated by ##v## is ##V##? This is certainly not true in general, since if ##T## is the zero transformation and ##V## has dimension greater than 1 then no T-cyclic subspace will equal ##V##.

But what about for an arbitrary linear map?

BiP

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# Generating a vector space via a T-cyclic subspace

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