Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T03:00:56.063Z Has data issue: false hasContentIssue false

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.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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