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XX.—The Theory of Orthogonants and Latent Roots from 1881 to 1918

Published online by Cambridge University Press:  15 September 2014

Thomas Muir
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Extract

The increased interest taken in Orthogonants during the period 1880–1900 is more than maintained in the period which we have now reached. Out of considerably more than 100 writings sought out and examined, as many as 65 have been found to deal directly with the theory of orthogonal substitution, and 35 to be more closely concerned with the practical applications of it. These numbers, 65 and 35, are what have to be set over against 38 and 12 in the earlier period referred to, note, however, at the same time being taken that the contrast is unfairly heightened by several papers of the first period, chiefly Magyar, having been received only in time to be joined with those of the second. These Magyar papers, it may be added, make also an appreciable contribution in the matter of quality.

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Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 47 , 1928 , pp. 252 - 282
Copyright
Copyright © Royal Society of Edinburgh 1928

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References

AUXILIARY LIST OF WRITINGS MAINLY APPLICATIONAL

1879 Weierstrass, C. “Nachtrag zu der Abhandlung” (Berl. Ber., 1858, pp. 202–220). “Ueber …,” Monatsb. … Akad. d. Wiss. (Berlin), 1879, pp. 430–439.Google Scholar
1884 Jacobi, C. G. J. “Bemerkungen zu einer Abhandlung Eulers über die orthogonale Substitution,” Gesammelte Werke iii, p. 601.Google Scholar
1887. Vályi, J. “Zur Lehre der quadratischen Formen,” Math. u. naturw. Berichte aus Ungarn, v, pp. 16–19 : or Archiv d. Math. u. Phys. (2), vi, pp. 445–448.Google Scholar
1890. Caspary, F. “Sur les relations qui lient les éléments d'une système orthogonal aux fonctions theta et sigma d'un seul argument et …,” Journ. (de Liouville) de Math. … (4), vi, pp. 367–404.Google Scholar
1891 15/3. Fröhlich, I. “Wechselseitige Anziehungen und Abstossungen gleichseitig schwingender Elementarmagnete,” Math. u. naturw. Berichte aus Ungarn, ix, pp. 90–137: in particular § 14 : or Értekezések a Math. Tudom. Köréböl, xiv, Nr. 5, pp. 1–44.Google Scholar
1891 Cornely, A. “Untersuchungen über involutorische Gleichungen,” Dissert., Würzburg.Google Scholar
1892. Rost, G. “Untersuchungen über die allgemeinste linearen Substitutionen deren Potenzen eine endliche Gruppe bilden,” 28 pp., Leipzig.Google Scholar
1893. Study, E. “Sphärische Trigonometrie, orthogonale Substitutionen und elliptische Funktionen,” Abhandlungen … Ges. d. Wiss., (Leipzig) xx, pp. 83–232.Google Scholar
1898 /11. Pap, P. “Adalek a lineár rokonságok elméletéhez,” Math, és phys. lapok, vii, pp. 321–325.Google Scholar
1899. Jahnke, E. “Nouvelles expressions des éléments d'un système orthogonal par les fonctions sigma d'un seul argument, et leur application …,” Journ. (de Liouville) de Math. … (5), v, pp. 155–174.Google Scholar
1900 14/3. Koch, H. v. “Sur la transformation des formes bilinéaires,” Öfversigt … Akad. Forhandl. (Stockholm), lvii, pp. 335–351.Google Scholar
1900 30/6. Loewy, A. “Ueber die Transformation einer Hermiteschen Form von nicht verschwindender Determinante in sich,” Göttinger Nachrichten, 1900, pp. 298–302.Google Scholar
1909 /9. MacMahon, P. A. “A property of the characteristic symbolic determinant of n quantics in n variables,” Report British Assoc. Adv. Sci. (1900), p. 644.Google Scholar
1900. Krause, M. “Zur Theorie der Thetafunktionen zweier veränderlicher Grössen,” Archiv d. Math. u. Phys. (3), i, pp. 64–68.Google Scholar
1902 /12. Nicoletti, O. “Su una classe di equazione a radici reali,” Annali di Mat. (3), ix, pp. 93–138.Google Scholar
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1904. Burnside, W. On linear substitutions of determinant unity with integral coefficients, Messenger of Math., xxxiii, pp. 133–137.Google Scholar
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1906. Hilbert, D. “Grundzüge einer allgemeiner Theorie der linearen Integralgleichungen,” Nachrichten … Ges. d. Wiss. (Göttingen) Ann., 1906, pp. 157–227, 439–480.Google Scholar
1906. Jahnke, E. “Aufgabe 167,” Archiv d. Math. u. Phys. (3), xi, p. 130.Google Scholar
1909. Widder, W. “Untersuchungen über die allgemeinste linearen Substitutionen mit vorgebener p ter Potenz,” Dissert. (Würzburg), 53 pp. Leipzig.Google Scholar
1911 4/9. Hilton, H. “The canonical form of an orthogonal substitution,” Report … British Assoc. …, lxxxi, p. 326.Google Scholar
1911. Hilton, H. “On cyclant substitutions,” Messenger of Math., xli, pp. 49–51.Google Scholar
1911. Hilton, H. “On invariants of a canonical substitution,” Proceed. London Math. Soc. (2), x, pp. 423–425; xi, pp. 96–103.Google Scholar
1912. Hilton, H. “On symmetrical and orthogonal substitutions,” Messenger of Math., xli, pp. 146–154.Google Scholar
1912. Potron, M. “Quelques propiétés des substitutions linéaires à coefficients ≷ 0, et …,” Comptes Rendus de l'Acad. des Sci. (Paris) cliii, pp. 1129–1132, 1458–1459.Google Scholar
1913. Jahnke, E. “Das Orthogonalsystem der Lorentz-Transformation” Rendic. del Circolo mat. …, xxxv, pp. 90–94 ; Sitzungsb. d. Berliner Math. Ges., xii, pp. 109–112.CrossRefGoogle Scholar
1914 14/6. Amato, V. “Le sostituzioni ortogonali periodiche,” Atti … Accad. Gioenia … (Catania) (5), vii, mem. 23, 11 pp.Google Scholar
1914 /6. Hilton, H. “Properties of certain homogeneous linear substitutions,” Annals of Math. (2), xv, pp. 195–201.Google Scholar
1914. Mahrenholz, J. “Lösung zur Aufgabe 436,” Archiv d. Math. u. Phys. (3), xxiii, pp. 185–187.Google Scholar
1914. Jahnke, E. “Ein Orthogonalsystem für die Thetafunktionen von drei Argumenten,” Festschrift-Schwarz, pp. 157–165.Google Scholar
1914. Hilton, H. “Homogeneous Linear Substitutions,” viii + 181 pp. Oxford.Google Scholar
1915 3/2. Amato, V. “Sulla forma canonica delle sostituzioni ortogonali periodiche,” Atti … Accad. Gioenia … (Catania) (5), viii, mem. 15, 8 pp.Google Scholar
1916. Lattès, S. “Sur une forme canonique nouvelle des substitutions linéaires,” Annales … des Sci. (Toulouse) (3), vi, pp. 1–84.Google Scholar
1916. Taber, H. “Conditions for the complete reducibility of groups of linear substitutions,” Amer. Journ. of Math., xxxviii, pp. 337–372.CrossRefGoogle Scholar