[R] Algebraic operation on the missing values

[Joanna Procelewska]

Hi all,

I have a large set of descriptors, which are stored as the vectors, each one
containing about 450 elements. Now I have to perform some algebraical
operations on this set to eliminate the redundant ones. The problem is, that
not all vales in the vectors are known. 
Are there any norm defined how should I process such vectors? Simple example:
having two vectors:
 
a      b
3      4
2      null
3      6
 
I can imagine that a+b is [7 null 9]', but what about scalar product? Is it
null or have it a value? 
I don't want to replace missing values with the concrete ones, but they
significantly complicate my computations. 

Does anyone know whether there are any ways to solve this problem?
Please share some experience. Really appreciate the help!

Sincerely,

Joanna