Abstract
The eigenvalue problem of a Hermitian quaternion matrix plays a crucial role in quaternion quantum mechanics because it is closely related to the solution of Schrödinger equation. In this paper, a fast algorithm is proposed for finding the eigenvalues and corresponding eigenvectors of a Hermitian quaternion matrix based on the real representation of a quaternion matrix as well as the special structure and properties of a Hermitian quaternion matrix. Numerical experiments demonstrate that, compared with the existing computational methods for the eigenvalue problem of a Hermitian quaternion matrix, the proposed method in this paper not only greatly improves the computational efficiency, but also achieves better experimental results in terms of the corresponding computational errors.
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