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V.—Factors of Circulants

Published online by Cambridge University Press:  15 September 2014

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Extract

1. Among the well-known theorems for the breaking up of a circulant into factors are the following:—

Theorem I.*—The circulant

where θ is one of the nth roots of unity.

Type
Proceedings
Copyright
Copyright © Royal Society of Edinburgh 1920

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References

page 41 note * Catalan, “Recherches sur les determinants,” Bull, de l'Acad. R. des Sci., etc., de Belgique, 1 sér., xiii.

page 41 note † Stern, , “Einige Bemerkungen über eine Determinante,” Crelle's Journal, lxxiii, pp. 374380Google Scholar.

page 41 note ‡ Catalan, loc. cit.

page 41 note § Mnir, , “On Circulants of Odd Order,” Quarterly Jour. Math., xviii, pp. 261265Google Scholar.

page 41 note ‖ Scott, , “Note on a Determinant Theorem of Mr Glaisher's,” Quarterly Jour. Math., xvii, pp. 129132Google Scholar.

page 41 note ¶ Torelli, , “Sui determinanti circolanti,” Rendic. Accad. delle Sci. Fis. e Mat. (Napoli), 1882, pp. 311.Google Scholar

page 42 note * Muir, , “On the Resolution of Circulants into Rational Factors,” Proc. Roy. Soc. Edin., xxi, 1896, pp. 369382.Google Scholar

page 42 note † Muir, , “A Special Circulant considered by Catalan,” Proc. Roy. Soc. Edin., xxiv, Part 6, 1903.Google Scholar