The reason eig wants two square matrices is that it calculates the similarity transformation matrix that maps one matrix from one coordinate system (set of bases) to another. You might be able to do that if you set your vectors up as companion-form matrices, but I doubt that would be of any real benefit.
In your application, you seem to me to have a simple linear transformation between two vectors (not matrices) that is most appropriate to polyfit:
vA = rand(10,1)
vB = vA*pi + exp(1)
B = polyfit(vA, vB, 1)
B =
3.1416e+000 2.7183e+000
There are many other functions that will do this, but the core MATLAB function polyfit is the simplest.
