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On a Normal Form of the Orthogonal Transformation I

Published online by Cambridge University Press:  20 November 2018

Hans Zassenhaus
Hans Zassenhaus*
Affiliation:
McGill University
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At the Edmonton Meeting of the Canadian Mathematical Congress E. Wigner asked me whether one knew something about the distribution of the characteristic roots of the linear transformations that leave invariant the quadratic form t2+x2-y2-z2, just as one knows that a Lorentz transformation has two complex conjugate characteristic roots and two real characteristic roots that are either inverse to one another or the numbers 1 and -1.

In this paper an answer to E. Wigner’s question will be obtained.

We are concerned with the pairs of matrices (X,A) with coefficients in a field of reference F such that the condition

0.1

is satisfied, where XT = (ξki) is the transpose of the matrix X = (ξki). It follows that both matrices are quadratic of the same degree d.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 1 , Issue 1 , 01 January 1958 , pp. 31 - 39
Copyright
Copyright © Canadian Mathematical Society 1958