Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-23T23:35:26.505Z Has data issue: false hasContentIssue false
  • English
  • Français

The expression of an infinite lower semi-matrix in terms of its idempotent and nilpotent elements

Published online by Cambridge University Press:  20 January 2009

C. E. Gurr  and
H. W. Turnbull
H. W. Turnbull
Affiliation:
Birkbeck College, London, E.C.4
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.

The importance of matric algebras in Function Theory and in Physics (Birtwistle—The new Quantum Mechanics; and Courant and Hilbert—Methoden der mathematischen Physik) has resulted in comprehensive works on finite matrices. Very little progress has, however, been made in the necessary algebras of infinite matrices.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 6 , Issue 2 , October 1939 , pp. 61 - 74
Copyright
Copyright © Edinburgh Mathematical Society 1939

References

BIBLOGRAPHY

1.Cooke, R. G., Some solutions of the matrix equation AX – XA = 1. Journal London Math. Soc., 8 (1933), 107–109.Google Scholar
2.Cooke, R. G., The transformation of some classes of infinite matrices into diagonal matrices. Journal London Math. Soc., 8 (1933), 167–175.Google Scholar
3.Dienes, P., The Taylor series (Oxford, 1931).Google Scholar
4.Dienes, P., The exponential function in linear algebras. Quarterly Journal (Oxford Series), 1 (1930), 300–309.Google Scholar
5.Dienes, P., Notes on Linear Equations in infinite matrices. Quarterly Journal (Oxford Series), 3 (1932), 253–268.Google Scholar
6.Hilton, H., Linear substitutions (Oxford, 1914).Google Scholar
7.Julia, G., Introduction mathématique aux théories quantiques (Paris, 1936).Google Scholar
8.Riesz, F., Les systemes d'equations linéaires a line infinité d'inconnues (Paris, 1913).Google Scholar
9.Turnbull, H. W., The theory of determinants, matrices and invariants (Blackie, 1928).Google Scholar
10.Turnbull, H. W. and Aitken, A. C., An introduction to the theory of canonical matrices (Blackie, 1932).Google Scholar
11.Volterra, V. and Hostinsky, B., Operations infinitesimales lineaires (Paris, 1938).Google Scholar
12.Wedderburn, J. H. M., Lectures on matrices (Amer. Math. Soc., New York, 1934).CrossRefGoogle Scholar