In this short paper, a matrix perturbation bound on the eigenvalues found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of two data matrices. The application of the theoretical analysis to multi-objective optimization problems (e.g., those arising in the design of acoustic metamaterial filters) is briefly discussed, together with possible extensions.

翻译：在这份简短的文件中,对主要组成部分分析所发现的电子元值的矩阵扰动进行了调查,因为主要组成部分分析所依据的数据矩阵是两个数据矩阵的组合组合,对将理论分析应用于多目标优化问题(例如,在声学元材料过滤器的设计中产生的问题)以及可能的扩展问题进行了简要讨论。