Vector Spaces, Polynomials "Over Fields"

[Seacow1988]

What does it mean when a vectors space is "over the field of complex numbers"? Does that mean that scalars used to multiply vectors within that vector space come from the set of complex numbers?

If so, what does it mean when a polynomial, p(x) is "over the field of complex numbers"?

Thanks!

[tiny-tim]

Hi Seacow1988! Welcome to PF! :smile:
What does it mean when a vectors space is "over the field of complex numbers"? Does that mean that scalars used to multiply vectors within that vector space come from the set of complex numbers?

Yup! :biggrin:
If so, what does it mean when a polynomial, p(x) is "over the field of complex numbers"?

p(x) = ∑ anxn where all the ans are complex numbers :wink: