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A theorem of Hurwitz and Radon and orthogonal projective modules
- Source :
- Proceedings of the American Mathematical Society. 42:51-56
- Publication Year :
- 1974
- Publisher :
- American Mathematical Society (AMS), 1974.
-
Abstract
- We find the maximum number of orthogonal skewsymmetric anticommuting integer matrices of order n for each natural number n and relate this to finding free direct summands of certain generic projective modules. While studying composition of quadratic forms, Hurwitz [4] and Radon [6] considered families of orthogonal matrices {A1,3L , A,} satisfying the conditions (1) Ai= -At, i= 1, ,s (2) AiAj = -AjAi, i $ j. DEFINITION. (1) A family of orthogonal matrices satisfying (1) and (2) above will be called a Hurwitz-Radon (H-R)family. If n is a positive integer and n=2ab, b odd, then we write a=4c+d where O0d
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 42
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi...........81f6081e40ba16486f72478106a4ce0e