Generation dynamics and load dynamics plays an important role in the small signal stability analysis of Microgrids, especially for the islanded operation mode. It is essential for a Microgrid to maintain small signal stability characteristics under small changes of operating conditions caused by generation variations or load fluctuations. In this paper, a novel approach based on matrix perturbation theory (MPT) is proposed for the computation of eigen-solutions in a perturbed Microgrid system. Rigorous theoretical analysis is conducted on the distinct and multiple eigenvalues and their corresponding eigenvectors respectively under perturbations of generation or load. The computational flowchart of the system eigen-solutions is then proposed, aimed at obtaining eigenvalues and eigenvectors of a perturbed system without solving an eigenvalue problem repeatedly. Finally, the effectiveness of the matrix perturbation based approach for eigen-solutions' analysis are tested via a low-voltage Microgrid prototype.