Not too sure what you mean by a matter wave.
A wave on the ocean is a wave in matter and since the matter is composed of atoms it's atoms which are oscillating.
The same is true of sound traveling through air, (but not forms of electromagntism, those travel through a field which exists regardless of any matter)
Editing ...
OK, I misunderstood what you meant, you were referring to the wave function proposed by Louis de Broglie.
I'll leave that for somebody more knowlegeable of the subject.