{1, x, 2x^2} is a basis for V (the polynomial vector space with maximum power 2)(adsbygoogle = window.adsbygoogle || []).push({});

then could I say that the coordinate vectors with respect to V, which form the set {(1,0,0), (0,1,0), (0,0,2)} for R^3 is equivalent to the above set in V?

Although the word equivalent is not defined. But it is true that any property one set has automatically implies to the other set? If yes then it seems it is much easier to work with the set in R^3.

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# Equivalent sets in different vector spaces?

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