Matter waves are mostly analogous to the other waves like material waves of oscillations in the medium about its equilibrium position.  One major difference is that matter waves have no polarization.

Lewis de-Broglie proposed that matter has dual characteristic just like radiation. It means when the matter is moving it shows the wave properties  are associated with it and when it is in the state of rest then it shows particle properties. Thus the matter has dual nature. The waves associated with moving particles are matter waves or de-Broglie waves.

Expression:  λ = h/p  (p = mv)      

This wavelength is called de-Broglie wavelength.