Hostname: page-component-669899f699-chc8l Total loading time: 0 Render date: 2025-04-25T19:53:45.273Z Has data issue: false hasContentIssue false
  • English
  • Français

XV.—Matrices and Continued Fractions, II

Published online by Cambridge University Press:  15 September 2014

H. W. Turnbull
Get access

Extract

This communication is a sequel to a former work (Proc. Roy. Soc. Edin., vol. liii, 1933, pp. 151–163). An explicit, and apparently new, form is given for the rational reduction of a matrix to diagonal form, applicable to symmetric matrices and also to continuants. An account follows which co-ordinates several existent theories of generalized continued fractions, and concludes with a few determinantal theorems as corollaries.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 53 , 1934 , pp. 208 - 219
Copyright
Copyright © Royal Society of Edinburgh 1934

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

References to Literature

1.Schweins, , 1825. Cf. Muir, History of Determinants, vol. i, p. 174.Google Scholar
2.Smith, H. J. S., 1860. British Association Report (1860). Collected Works, vol. i, p. 408.Google Scholar
3.Richardson, A. R., 1928. Proc. London Math. Soc., (2), vol. xxviii, pp. 395—420.Google Scholar
4.Sylvester, , 1853. Phil. Mag., (4), vol. v, p. 446 and vol. vi, p. 297. Collected Works, vol. i, pp. 609, 641.CrossRefGoogle Scholar
5.Paley, and Ursell, , 1929. Proc. Cambridge Phil. Soc., vol. xxvi, pp. 127–144.Google Scholar
6.Milne-Thomson, , 1933. Proc. Edin. Math. Soc., (2), vol.iii, pp. 189–200.CrossRefGoogle Scholar
7.Whittaker, E. T., 1916. Proc. Roy. Soc. Edin., vol. xxxvi, pp. 243–255.Google Scholar
8.Turnbull, , 1933. Proc. Roy. Soc. Edin., vol. liii, pp. 151–163.Google Scholar
9.Heilermann, , 1845. Journ. für Math., vol. xxxiii, p. 174.Google Scholar
10.Perron, , 1907. Math. Annalen, vol. lxiv, p. 1, who gives many references to Jacobi and others.CrossRefGoogle Scholar