I'm curious that: Are $\Bbb C^4$ and polynomials of degree at most five isomorphic vector spaces? Thanks a lot.
2026-03-26 19:18:27.1774552707
Are $\Bbb C^4 $and polynomials of degree at most five isomorphic vector spaces?
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You are taking $\Bbb C^4$ as a vector over $\Bbb C$ right ? Then both your vector spaces will have different dimensions hence not isomorphic.
Edit: It doesn't matter you are considering $\Bbb C^4$ as a vector over $\Bbb C$ or $\Bbb R$, in any case it will have different dimension to polynomials of degree at most 5.