Carlos,

I have used the built-in vector operations found in the documentation:

Vector Tutorial

Vector Guide

Operations on Vectors

Is this what you want? These operations all work on symbolic vectors and should do what you want unless I am not understanding your request.

Regards,

Neil

Carlos,

That should be Ok. The only issue that I have ever encountered is that you need to use variables in the matrix so WMA knows the dimensionality of your problem. For example, I would be careful using a single variable for a matrix because some operations assume the variables as scalars (or more accurately, they can handle either scalar or matrix arguments so a single variable is assumed to be scalar). So set k={{a,b},{c,d}} or k=Array[a,{2,2}]

Your equations can then be expressed using MatrixExp[], Div, Cross, Grad, etc

Documentation is here: Vector Analysis