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Linear Transformations Preserving the Real Orthogonal Group

Published online by Cambridge University Press:  20 November 2018

Albert Wei
Albert Wei*
Affiliation:
University of Toronto, Toronto, Ontario
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Let K be a field and Mn﹛K) denote the vector space of n X n matrices over K. Marcus [4] posed the following general problem: Let W be a subspace of Mn(K) and S a subset of W. Describe the set L(S, W) of all linear transformations T on W such that T(S) is contained in S.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 561 - 572
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Dieudonné, J., Sur une généralisation du groupe orthogonal a quatre variables, Arch. Math. 1 (1949), 282–287.Google Scholar
2. Hurwitz, A., Ùber die Komposition der quadratischer Formen, Math. Ann. 88 (1923), 1–25.Google Scholar
3. Marcus, M., All linear operators leaving the unitary group invariant, Duke Math. J. 26 (1959), 155–163.Google Scholar
4. Marcus, M., Linear operations on matrices, Amer. Math. Monthly 69 (1962), 837–847.Google Scholar
5. Marcus, M., Linear transformations on matrices, J. Res. Nat. Bur. Standards Sect. B 75 (1971), 107–189.Google Scholar
6. Marcus, M. and Moyls, B., Transformations on tensor product spaces, Pacific J. Math. 9 (1959), 1215–1221.Google Scholar
7. Radon, J., Lineare Scharen orthogonaler Matrizen, Abh. Math. Sem. Univ. Hamburg I (1923), 1–14.Google Scholar
8. Wallis, J., Hadamard designs, Bull. Austral. Math. Soc. 2 (1970), 45–55.Google Scholar