Assuming all of the "vectors" are the same length (if they aren't, then the result will be the same length as the shortest):
(For some reason the "plus" in the expression above is getting converted to the XML entity notation? But not in the editor Preview...)
List<double[]> lstVectors = ...;
double[] vectorSum = lstVectors.Aggregate((a,b) => a.Zip(b, (aa, bb) => aa + bb).ToArray());
Not the most efficient, but it ought to do the job.(For some reason the "plus" in the expression above is getting converted to the XML entity notation? But not in the editor Preview...)