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Vanishing Aggregates of Determinant Minors
Published online by Cambridge University Press: 15 September 2014
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1. Since a persymmetric determinant is a particular case of an axisymmetric determinant, it follows that every type of vanishing aggregate for axisymmetric determinants is also a vanishing aggregate for persymmetric determinants. The principal object of this paper is to give a series of theorems (I., II., III., IV., V.), by the application of which to any vanishing aggregate of minors of persymmetric determinants new vanishing aggregates are obtained (7–12), which, though true for persymmetric, are no longer true for axisymmetric determinants.
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- Copyright © Royal Society of Edinburgh 1906
References
page 853 note * Muir, , “Vanishing Aggregates of Secondary Minors of a Persymmetric Determinant, “Trans. Roy. Soc. Edin., vol. xl., 1902.Google Scholar This will be referred to hereafter as Muir, paper I.
page 853 note † Metzler, , “On Certain Aggregates of Determinant Minors,” Trans, Amer. Math. Soc., October 1901.CrossRefGoogle Scholar Referred to hereafter as Metzler, paper I.
page 853 note ‡ Kronecker, , “Die Subdeterminanten Symmetricher Systeme,” Berliner Berichte, 1882.Google Scholar
page 853 note § Metzler, l.c., paper I.
page 853 note ‖ Muir, , “Aggregates of Minors of an Axisymmetric Determinant,” Phil. Mag., April 1902.CrossRefGoogle Scholar Referred to hereafter as Muir, paper II.
page 854 note * Nansen, , “Minors of Axisymmetric Determinants, “Amer. Jour. of Math., January 1905.CrossRefGoogle Scholar— Metzler, , “Variant Forms of Vanishing Aggregates of Minors of Axisymmetric Determinants,” Proc. Roy. Soc. Edin., XXV., 1905, p. 717.Google Scholar
page 854 note † Muir, , “The Automorphic Linear Transformation of a Quadric,” Trans. Roy. Soc. Edin., xxxix. L.c., paper I., theorem (A).Google Scholar
page 854 note ‡ Tito, Cazzaniga, “Relazioni fra i minori di un determinante di Hankel,” Rendiconti del R. Ist. Lomb. di sc., e lett., Serie ii., vol. xxxi., 1898.Google Scholar
page 854 note § Muir, , l.c., paper I. “The Law of Extensible Minors and Certain Determinants,” Proc. Edin. Math. Soc., vol. xx., 1901–1902.Google Scholar
page 855 note * Metzler, l.c., paper I., theorem (1).
page 857 note * Metzler, l.c., paper I. theorem (2).
page 858 note † L.c., paper I. arts. 17 to 28.