i store the position of an object in 3d space in a 4by4 transformation matrix. now in order to move the object from the position stored in matrix A to the position stored in
Just interpolating the matrix values likely won't give you what you want unless you're only doing very simple transformations (for example, translation or scaling).
I think there are methods that decompose a matrix into translation, rotation, scaling, etc. and then you could build new matrices that interpolate based on those parameters.
You could also just do a before and after transformation, and then lerp the verts of the object. This may also not give you the results you're after.