Abstract
Concerning of invariant subspaces, we must bring up its relative perturbation theorems. In 1999, Q. F. Xu characterized periodic invariant subspaces clearly. Moreover, W. W. Lin and C. S. Wang had algorithm to compute periodic invariant subspaces numerically. Hence, with this process, we want to analyze its error bound. This paper is therefore produced. In this paper, we first introduces the concepts of the eigenvalue, eigenvector, eigenspace, simple eigenspace for regular periodic matrix pairs. Then, we reduce periodic matrix pairs to Schur form or canonical form via equivalence transfomations. Finally, we perturb the eigenspaces and simple eigenspaces, and then estimate the error bound. We show the results and ensure that it is the same with those for general cases.