Matrix operations

Hi! I am learning C++, and I am trying to understand how operators
work, and should work. So, I've decided to do yet another matrix class!
Anyway, I'm stuck with deciding how I should implement things here,
mainly regarding operator overloading.

What I've done so far is this:

class cmatrix
{
public:
   explicit cmatrix(unsigned int rows, unsigned int cols);
   explicit cmatrix(cmatrix& src);
   virtual ~cmatrix();
   virtual double& at(unsigned int r, unsigned int c);
   virtual cmatrix& operator=(const cmatrix src);
private:
   vector<unsigned int, double> storage;
};

and I've successfully implemented the operator= (or better: it works),
but now I've doubts with other operations! Before that, is my copy
constructor well defined? And a silly question... does the operator=
need a reference, or is it ok to leave it as I wrote?

My question is easy: how do I multiply two matrices? I mean, in the
"definition" sense, this is not an algorithmic doubt! Let's suppose I
want to write this:

M = N * Q;

with M, N, and Q being cmatrix instances. That is the equivalent,
according to Stroustrup's book, of

M.operator=(N.operator*(Q));

The problem is... How should I declare the operator* ? I don't want to
modify N, and I'd like to avoid pointers! Forgive this silly question,
but I'm still learning! :)

Another problem is with cvector, derived from cmatrix. Will the same
operator work? Like:

v = M * w;

or worse, what if I want to overwrite a cvector or cmatrix?

v = M * v;

Thanks for any help you can give me!