In this sense, the method has advantages in computational cost and storage capacity. In the non-self-adjoint case, an algebraic method is presented to determine the eigensolution derivatives directly and simultaneously without having to use the left eigenvectors. In the self-adjoint case, a direct algebraic method is presented to determine the eigensolution derivatives simultaneously by solving a linear system with a symmetric coefficient matrix. Then a unified consideration of the computation of the sensitivity and Hessian matrix is studied for both the self-adjoint and non-self-adjoint cases. A generalized eigenproblem is formed and its normalizations are presented and discussed.
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