The quaternionic determinant

Electronic Journal of Linear Algebra

Volumn 7, Issue , 2000, Pages 100-111

  Cohen, Nir ^a   De Leo, Stefano ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Determinant; Matrices; Quaternions

Indexed keywords

EID: 0007249376     PISSN: 10813810     EISSN: None     Source Type: Journal    
DOI: 10.13001/1081-3810.1050     Document Type: Article

References (36)

1. D. Finkelstein, J. M. Jauch, and D. Speiser. Notes on quaternion quantum mechanics. In C. A. Hoker, ed., Logico-Algebraic Approach to Quantum Mechanics. Reidel, Dordrecht, 1979, pages 367-421.
2. D. Finkelstein, J. M. Jauch, S. Schiminovich, and D. Speiser. Foundations of quaternion quantum mechanics. J. Math. Phys., 3:207-220, 1962.
3. D. Finkelstein, J. M. Jauch, and D. Speiser. Quaternionic representations of compact groups. J. Math. Phys., 4:136-140, 1963.
4. S. L. Adler. Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, New York, 1995.
5. G. M. Dixon, Division Algebras: Octonions, Complex Numbers and the Algebraic Design of Physics. Kluwer Academic Publishers, Boston, 1994.
6. S. De Leo and W. A. Rodrigues. Quantum mechanics: From complex to complexified quaternions. Internat. J. Theoret. Phys. 36:2725-2757, 1997.
7. S. De Leo and G. Scolarici. Right eigenvalue equation in quaternionic quantum mechanics. J. Math. Phys A., 33:2971-2995, 2000.
8. N. W. Johnson and A. I. Weiss. Quaternionic modular groups. Linear Algebra Appl., 295:159-189, 1999.
9. S. De Leo. Quaternion and special relativity. J. Math. Phys., 37:2955-2968, 1996.
10. S. De Leo and G. Ducati. Quaternionic group in physics. Internat. J. Theoret. Phys., 38:2195-2218, 1999.
11. S. De Leo. Quaternions for GUTs. Internat. J. Theoret. Phys., 35:1821-1837, 1996.
12. S. De Leo and P. Rotelli. Quaternionic electroweak theory. J. Phys. G, 22:1137-1150, 1996.
13. A. Cayley. The Collected Mathematical Papers. Cambridge University Press, Cambridge, 1989, Vol. 1:123-126.
14. E. Study. Zur Theorie der linearen Gleichungen. Acta Math., 42:1-61, 1920.
15. J. Dieudonné. Les déterminants sur un corp non-commutatif. Bull. Soc. Math. France, 71:27-45, 1943.
16. H. Aslaksen. Quaternionic determinants. Math. Intelligencer, 18(3):57-65, 1996.
17. F. Zhang. Quaternions and matrices of quaternions. Linear Algebra Appl., 251:21-57, 1997.
18. N. A. Wiegmann. Some theorems on matrices with real quaternion elements. Canad. J. Math., 7:191-201, 1955.
19. P. M. Cohn. The similarity reduction of matrices over a skew field. Math. Z., 132:151-163, 1973.
20. S. De Leo and P. Rotelli. Translations between quaternion and complex quantum mechanics Progr. Theoret. Phys., 92:917-926, 1994.
21. S. De Leo and P. Rotelli. Odd dimensional translation between complex and quaternionic quantum mechanics. Progr. Theoret. Phys., 96:247-255, 1996.
22. L. X. Chen. Inverse matrix and properties of double determinant over quaternionic field. Sci. China, 34:528-540, 1991.
23. W. R. Hamilton. The Mathematical Papers of Sir William Rowan Hamilton. Cambridge University Press, Cambridge, 1967.
24. W. R. Hamilton. Elements of Quaternions. Chelsea Publishing Co., New York, 1969.
25. I. Niven. Equations in quaternions. Amer. Math. Monthly, 48:654-661, 1941.
26. I. Niven. The roots of a quaternion. Amer. Math. Monthly, 49:386-388, 1942.
27. L. Brand. The roots of a quaternion. Amer. Math. Monthly, 49:519-520, 1942.
28. S. Eilenberg and I. Niven. The fundamental theorem of algebra for quaternions. Bull. Amer. Math. Soc., 52:246-248, 1944.
29. A. Baker. Right eigenvalues for quaternionic matrices: A topological approach. Linear Algebra Appl., 286:303-309, 1999.
30. R. Von Kippenhahn. Über den Wertevorrat einer Matrix. Math. Nachr., 6:193-228, 1951.
31. L. A. Wolf. Similarity of matrices in which the elements are real quaternions. Bull. Amer. Math. Soc., 42:737-743, 1936.
32. J. Brenner. Applications of the Dieudonné determinant. Linear Algebra Appl., 1:511-536, 1968.
33. H. C. Lee. Eigenvalues and canonical forms of matrices with quaternion coefficients. Proc. Roy. Irish Acad. Sect. A, 52:253-260, 1949.
34. J. L. Brenner, Matrices of quaternions. Pacific J. Math., 1:329-335, 1951.
35. R. A. Horn and C. R. Johnson. Topics in Matrix Analysis. Cambridge University Press, Cambridge, 1994.
36. F. Gürsey and C. H. Tze. On the Role of Division, Jordan and Related Algebras in Particle Physics. World Scientific, Singapore, 1996.