Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study the analyticity of the semisimple eigenvalue and the corresponding eigenvector functions of general analytic matrix-valued functions which are very important in many engineering applications such as the optimum design of dynamical structures, model updating, damage detecting, quantum mechanics, diffraction grating theory, medical imaging, and social network theory.  establish some new sufficient conditions on existence of analytic eigenvalue and eigenvector functions corresponding to semisimple eigenvalues of general analytic matrix-valued functions, which relaxes the condition in [P. Lancaster, A. S. Markus, and F. Zhou, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 606--626].  also present a numerical method to compute the derivatives of the eigenvalue and eigenvector functions. Numerical performance of the method is illustrated by some numerical examples.
['Jiang Qian', 'Delin Chu', 'Roger C. E. Tan']
I am writing a research paper on a idea Analyticity of Semisimple Eigenvalues and Corresponding Eigenvectors of Matrix-Valued Functions
[{"from": "human", "value": "I am writing a research paper on a idea Analyticity of Semisimple Eigenvalues and Corresponding Eigenvectors of Matrix-Valued Functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study the analyticity of the semisimple eigenvalue and the corresponding eigenvector functions of general analytic matrix-valued functions which are very important in many engineering applications such as the optimum design of dynamical structures, model updating, damage detecting, quantum mechanics, diffraction grating theory, medical imaging, and social network theory.  establish some new sufficient conditions on existence of analytic eigenvalue and eigenvector functions corresponding to semisimple eigenvalues of general analytic matrix-valued functions, which relaxes the condition in [P. Lancaster, A. S. Markus, and F. Zhou, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 606--626].  also present a numerical method to compute the derivatives of the eigenvalue and eigenvector functions. Numerical performance of the method is illustrated by some numerical examples."}]