My professor uses the notation Hom(V,[itex]\mathbb{R}[/itex]) for the dual space of V. I usually see V* rather. What does the notation Hom(V,[itex]\mathbb{R}[/itex]) stands for exactly? I suppose the domain of Hom is wider than just (vector spaces) x (their field).(adsbygoogle = window.adsbygoogle || []).push({});

The notation suggest it is the set of homomorphisms btw V and R, but this would not accurately describe V* because we want the elements of V* to be linear fct, not just group homomorphisms (we need the f(av)=af(v) part of linear too).

So does the notation comes from a more category theory perspective, where linear maps are considered as "vector space homomorphisms" or something like that?

Just thoughts. I just wanna know what the general meaning for Hom is. Thx

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# Another notation for the dual space

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