sadly not been able to put much effort into this one! was a lecture i missed towards the end of term and didnt get the notes on it, however here is the question.(adsbygoogle = window.adsbygoogle || []).push({});

for K>or equal to 1 let P_{k}denote the the vector space of all real polynomials of degree at most k. For which value of n is P_{k}isomorphic to R^{n}. Give a brief reason for your answer.

Now from what i have found on two vector spaces being isomorphic they need to have equal dimensions (dimu=dimv) so knowing that we have dimR^{n})=n is as far as i have got. Not really understanding this one, surely they would be isomorphic at any value of n as long as it's between 1 and k????

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# Two vector spaces being isomorphic

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