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Another proof of the theorems on the eigenvalues of a square quaternion matrix

Published online by Cambridge University Press:  18 May 2009

Yik-Hoi Au Yeung
Yik-Hoi Au Yeung
Affiliation:
University of Hong Kong
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The nature of the eigenvalues of a square quaternion matrix had been considered by Lee [1] and Brenner [2]. In this paper the author gives another elementary proof of the theorems on the eigenvalues of a square quaternion matrix by considering the equation Gy = μȳ, where G is an n x n complex matrix, y is a non-zero vector in Cn, μ is a complex number, and ȳ is the conjugate of y. The author wishes to thank Professor Y. C. Wong for his supervision during the preparation of this paper.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 4 , July 1964 , pp. 191 - 195
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

References

REFERENCES

1.Lee, H. C., Eigenvalues and canonical forms of matrices with quaternion coefficients, Proc. Roy. Irish Acad. Sect. A, 52 (1949), 253–260.Google Scholar
2.Brenner, J. L., Matrices of quaternions, Pacific J. Math. 1 (1951), 329–335.CrossRefGoogle Scholar
3.Chevalley, C., Theory of Lie groups (Princeton, 1946).Google Scholar