Multi-Dimensional Sensitivity Analysis for Eigenvalue Problem of General Matrices
Zhang Yimin(1),Liu Qiaoling(1),Wen Bangchun(2)
(1 Department of Mechanics, Nanling Campus, Jilin University, Changchun, 130025, P . R. China)
(2 School of Mechanical Engineering, Northeastern University, Shenyang, 110006, P. R. China)

Abstract: The Kronecker algebra and the matrix calculus are employed to systematically develop generalized mathematical formulae for matrix sensitivity analysis of eigenvalue problem with general matrices. The derivatives of eigenvalues and eigenvectors are conveniently arranged into some 2D matrices. The results derived are easily amenable to computational procedures. 
Keywords: general matrix, eigenvalue problem, multi-dimensional sensitivity analysis, design variable matrix.