What is the difference between a vector space and a set.

Question

anonymous · Answer

a raft of axioms that have to be satisfied, as well as a couple of operations

anonymous · Answer

a set in general is just a collection of "objects" with or without any  condition imposed on the members of the set.
Vector space is also kind of set, but with special condition to be satisfied by the elements that belong to it.

anonymous · Answer

conditions*

unklerhaukus · Answer

which conditions, axioms, operations, are usually not common to vector spaces and sets

anonymous · Answer

http://en.wikipedia.org/wiki/Vector_space

unklerhaukus · Answer

is the set of complex numbers a vector space?

anonymous · Answer

yes

unklerhaukus · Answer

what about the set on n dimensional matrices ?

unklerhaukus · Answer

n dimensional complex  matrices ?

anonymous · Answer

also

unklerhaukus · Answer

are you sure

unklerhaukus · Answer

*^       n by n  complex  matrices ?

anonymous · Answer

can you add 2 by n complex matrices and get an n by n complex matrix? can you multiply an n by n complex matrix by a scalar (a real number would be a simple scalar to use here maybe) and get an n by n complex matrix as a result?

If the answer is yes to both questions, I think that means that n by n complex matrices make up a vector space. If I am wrong I would like to be corrected.