A similarity parameter between two polarimetriccoherency matrices is proposed based on matrix theory. This parametercan be applied not only to the data case of one-look polarimetricSynthetic aperture radar (SAR), but also to the case ofmulti-look polarimetric SAR. Several properties of the similarityparameter and the analysis on one-look and multi-look polarimetric dataare presented. As an application, target detection for multi-lookpolarimetric SAR case is discussed. Three kinds of improved powermaximization synthesis detector are proposed. Finally, the experimentalresult of target detection is presented and analyzed.