Higher algebra problems in universities. C is a linear vector space in complex number field. Why can it be defined on both C and R?

In which domain the vector space is located, the key is whether its multiplication operation in that domain is closed or not.

If V is a vector space on complex field C, then the linear combination of elements in V (with coefficients in C) is still in V. 。

Naturally, when the combination coefficient is in R, the linear combination is still in V 。

At this point, the eight algorithms are also established.

So your proposal stands.

If you are satisfied, please adopt it.