Grey incidence analysis (GIA), a branch of grey system theory, is commonly used in a broad range of scientific disciplines, from natural to social sciences. Since most current research on GIA models for panel data focuses on improving them, the mathematical principles and physical interpretations receive relatively limited attention. The principles of grey matrix incidence analysis (GMIA), which allows for both cross-sectional and time-series characteristics of panel data, are proposed in this paper. The panel data is first represented as a matrix, and then the matrix incidence operators are presented, along with theoretical properties and physical interpretations. The modeling principles, including the normativity, closeness, and column permutation independence, are articulated mathematically in a concise manner. The unified representation of GMIA models is then suggested, and the comprehensive procedures for expanding the GIA models for time series into the GMIA models for panel data are illustrated using the generalized GIA model as an example. Finally, the findings of the two examples indicate that the proposed solution has interpretability and robustness advantages over the compared approaches.