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Congruence Relations Between the Traces of Matrix Powers

Published online by Cambridge University Press:  20 November 2018

J. S Frame
J. S Frame*
Affiliation:
Michigan State College
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Extract

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Let A be a matrix of finite order n and finite degree d, whose characteristic roots are certain nth roots of unity a1, a2…, ad. We wish to prove a congruence (6) between the traces (tr) of certain powers of A, which is suggested by two somewhat simpler congruences (1) and (3). First, if tr (A) is a rational integer, it is easy to establish the familiar congruence

even though tr(Ap) may not itself be rational.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 3 , 01 June 1949 , pp. 303 - 304
Copyright
Copyright © Canadian Mathematical Society 1949

References

1 I am indebted to Professor R. Brauer for some suggestions for shortening my original proof.