Eigenvectors from eigenvalues in quaternion matrix with computer realization

02/16/2022

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by   Yuchao He, et al.

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In this paper, we extend eigenvector-eigenvalue identity (formally named by Peter B. Denton, Stephen J. Parker, Terence Tao, Xining Zhang <cit.>) to the quaternion division ring. A version of eigenvector-eigenvalue identity for the quaternion matrix is established. Furthermore, we give a new method and algorithm to compute the eigenvectors from the right eigenvalues for the quaternion Hermitian matrix. A program is designed to realize the algorithm to compute the eigenvectors. An open problem ends the paper. Some examples show a good performance of the algorithm and the program.