Quaternion involutions and anti-involutions

Computers and Mathematics with Applications

Volumn 53, Issue 1, 2007, Pages 137-143

  Ell, Todd A ^a   Sangwine, Stephen J ^b  

^a University of Essex ^*  (United States)

^b UNIVERSITY OF ESSEX   (United Kingdom)

Author keywords

Anti involution; Involution; Quaternion

Indexed keywords

COMPUTATIONAL COMPLEXITY; GEOMETRY; THEOREM PROVING;

ANTI INVOLUTION; QUATERNION INVOLUTIONS; SELF INVERSE LINEAR MAPPING;

CONFORMAL MAPPING;

EID: 34047251136     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.10.029     Document Type: Article

References (18)

1. W.R. Hamilton, On a new species of imaginary quantities connected with the theory of quaternions, in: Halberstam and Ingram [18], pp. 111-116 (Chapter 5). First published as [2]
2. Hamilton W.R. On a new species of imaginary quantities connected with the theory of quaternions. Proceedings of the Royal Irish Academy 2 (1844) 424-434
3. Ward J.P. Quaternions and Cayley Numbers: Algebra and Applications. Mathematics and its Applications vol. 403 (1997), Kluwer, Dordrecht
4. O'Meara O.T. Introduction to Quadratic Forms. Grundlehren der Mathematischen Wissenschaften vol. 117 (1963), Springer-Verlag, Berlin, Heidelberg, New York Reprinted with corrections 1971
5. W.R. Hamilton, Researches respecting quaternions. First series (1843), in: Halberstam and Ingram [18], pp. 159-226 (Chapter 7). First published as [6]
6. Hamilton W.R. Researches respecting quaternions. Transactions of the Royal Irish Academy 21 (1848) 199-296
7. Herstein I.N. Rings with Involution. Chicago Lectures in Mathematics (1969), University of Chicago Press, Chicago, London
8. In: Hazewinkel M. (Ed). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet 'Mathematical Encyclopaedia' (1988-1994), Kluwer, Dordrecht
9. Coxeter H.S.M. Quaternions and reflections. American Mathematical Monthly 53 3 (1946) 136-146
10. Benn I.M., and Tucker R.W. An Introduction to Spinors and Geometry with Applications in Physics (1987), Adam Hilger/IOP Publishing, Bristol, New York
11. W.R. Hamilton, On quaternions, in: Halberstam and Ingram [18], pp. 227-297 (Chapter 8). First published in various articles in Philosophical Magazine. pp. 1844-1850
12. V.M. Chernov, Discrete orthogonal transforms with data representation in composition algebras, in: Proceedings Scandinavian Conference on Image Analysis, Uppsala, Sweden, 1995, pp. 357-364
13. T. Bülow, Hypercomplex spectral signal representations for the processing and analysis of images, Ph.D. Thesis, University of Kiel, Germany 1999
14. Bülow T., and Sommer G. Hypercomplex signals - A novel extension of the analytic signal to the multidimensional case. IEEE Transactions on Signal Processing 49 11 (2001) 2844-2852
15. Mackey N. Hamilton and Jacobi meet again - quaternions and the eigenvalue problem. SIAM Journal on Matrix Analysis and Applications 16 2 (1995) 421-435
16. Fassbender H., Mackey D.S., and Mackey N. Hamilton and Jacobi come full circle: Jacobi algorithms for structured hamiltonian eigenproblems. Linear Algebra and its Applications 332 (2001) 37-80
17. T.A. Ell, S.J. Sangwine, Hypercomplex Wiener-Khintchine theorem with application to color image correlation, in: IEEE International Conference on Image Processing, ICIP 2000, vol. II, Institute of Electrical and Electronics Engineers, Vancouver, Canada, 2000, pp. 792-795
18. In: Halberstam H., and Ingram R.E. (Eds). The Mathematical Papers of Sir William Rowan Hamilton, Vol. III Algebra (1967), Cambridge University Press, Cambridge