A note on quaternion matrices and split quaternion matrix pencils

Ali, Istkhar

doi:10.1007/s12190-017-1147-7

Cited by 4 publications

(1 citation statement)

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“…In summary, based on the important role of split quaternions on mechanical systems, the study of the generalized eigen-problem of split quaternion matrices is urgent and necessary. In the paper [17], the authors deduced the existence of the generalized eigenvalues of the split quaternion matrices and gave a method for finding the complex eigenvalues of split quaternion matrices. However, it seems that the discussion and study of the problem of generalized eigenvalues of split quaternion matrices is not limited to complex values.…”

Section: Introductionmentioning

confidence: 99%

Algebraic algorithms for a class of Schrödinger equations in split quaternionic mechanics

Jiang,

Wang,

Guo

et al. 2024

Math Methods in App Sciences

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With the breakthroughs made by physicists in high‐dimensional mathematics, it has become possible to represent and solve a number of classical mathematical physics problems using the split quaternion algebra. In this paper, we study the least squares approximation of a class of Schrödinger equations in split quaternionic mechanics and propose two algebraic algorithms to the generalized right eigen‐problem for an i‐Hermitian split quaternion matrix pencil by using two isomorphic mappings. Numerical examples show the effectiveness of the proposed theories and algorithms.

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Section: Introductionmentioning

confidence: 99%