An algebraic algorithm for the diagonalization of a biquaternion matrix in the biquaternionic mechanics. (English) Zbl 07862453
Summary: Biquaternion algebra is an algebraic structure originating from a complex number and has mainly been used in quantum mechanics, special and general relativity, classical, relativistic, and covariant electrodynamics, and signal processing. In this paper, the problem of the diagonalization of a biquaternion matrix is studied, by means of a complex representation of a biquaternion matrix, and an algebraic algorithm for the diagonalization of a biquaternion matrix is presented. In addition, numerical examples demonstrate the effectiveness of the algebraic algorithm.
MSC:
| 11R52 | Quaternion and other division algebras: arithmetic, zeta functions |
| 15B33 | Matrices over special rings (quaternions, finite fields, etc.) |
| 15A20 | Diagonalization, Jordan forms |
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