TITLE: What is the main difference between a vector space and a field?
QUESTION [63 upvotes]: In my opinion both are almost same. However there should be some differenes like any two elements can be multiplied in a field but it is not allowed in vector space as only scalar multiplication is allowed where scalars are from the field.
Could anyone give me atleast one counter- example where field and vector space are both same.
Every field is a vector space but not every vectorspace is a field.
I need an example for which a vector space is also a field.
Thanks in advance. (I'm not from mathematical background.)

REPLY [3 votes]: For the sake of intuition, we can think of a field as R or C, and we can think of a vector space as R$^n$ for any natural number $n$.
More generally, for any field F, and for any $n\in$ N, F$^n$ is a vector space over F.
Note that a field is a type of vector space.