First- and second-order eigensensitivities of matrices with distinct eigenvalues
Yen-Lei Ling, BOR-CHYUN WANG · International Journal of Systems Science · 1988
Formulae for computation of the first- and second-order sensitivity matrices of the eigenvalues and eigenvectors of a matrix with distinct eigenvalues are derived using matrix calculus and the algebra of Kronecker products. The sensitivities of eigenvalues and eigenvectors to all elements of the matrix can thus be expressed by concise matrix equations.