In this paper, we propose a new approach for vector-sensor signal modeling and processing. We introduce the way quaternions allows to characterize signals collected on vector-sensor array. In physics or geophysics, vector signals contain several informations, like waveform (or source wavelet) and polarization. In order to access to the physical informations carried by the different wave fields recorded, it is necessary to develop wave or source separation techniques. So, we give here the extension to the quaternion case of a widely used tool in signal processing : the Singular Value Decomposition. We expose the way it can be computed, and develop a quaternionic subspace method for polarized wave separation using this new tool based on quaternion matrix algebra. We finally show on synthetic data the potentiality of this new quaternionic signal processing technique.