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On the extension of Fermat's theorem to matrices of order n

Published online by Cambridge University Press:  20 January 2009

J. B. Marshall
Affiliation:
Mathematical Institute, 16 Chambers street, Edinburgh, 1.
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It is proposed to establish, by elementary methods, a theorem for matrices analogous to Fermat's Theorem in the Theory of Numbers. In Jordan's Traité des Substitutions (Paris, 1870) pp. 127, 128, the order of any given linear substitution or matrix A with reference to any prime number p is determined, but the result given depends on the particular characteristic equation satisfied by the matrix A, and a general result applicable to all matrices of n rows and n columns does not seem to have been published hitherto.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1939