Vector Spaces, Polynomials Over Fields

[Seacow1988]

Vector Spaces, Polynomials "Over Fields"

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]

Welcome to PF!

Hi Seacow1988! Welcome to PF!

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!

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

p(x) = ∑ a_nxⁿ where all the a_ns are complex numbers