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A Note an a Group Defined by a Quadratic Form

Published online by Cambridge University Press:  20 November 2018

Marvin Marcus  and
Nisar A. Khan
Marvin Marcus
Affiliation:
The University of British Columbia, Muslim University, Aligarh, India
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In a recent series of papers [3,4,5], H. Zassenhaus considered the structure of those linear transformations T on real 4-space, R4, into itself that preserve the quadratic form . That is,

1.1

Define a function ϕ on R4 to the space M 2 of 2-square matrices over the complex numbers as follows:

1.2

Let G2 be the vector space of matrices generated by all real linear combinations of

1.3

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 2 , 01 May 1960 , pp. 143 - 148
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Dieudonné, J., Sur une généralisation du groupe orthogonal à quatre variables. Arch. Math. 1 (1949), 282-287.Google Scholar
2. Marcus, M. and Moyls, B. N., Linear transformations on algebras of matrices I, Canad. J. Math. 11 (1959), 61-66.Google Scholar
3. Zassenhaus, H. J., On a normal form of the orthogonal transformation I, Canad. Math. Bull. 1 (1958), 31-39.Google Scholar
4. Zassenhaus, H. J., On a normal form of the orthogonal transformation II, Canad. Math. Ball. 1 (1958), 101-111.Google Scholar
5. Zassenhaus, H. J., On a normal form of the orthogonal transformation III, Canad. Math. Bull. 1 (1958), 183-191.Google Scholar