Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-06T15:11:55.141Z Has data issue: false hasContentIssue false

The Asymptotic Value of the Volume of a Certain Set of Matrices

Published online by Cambridge University Press:  20 January 2009

Henry Jack
Affiliation:
Queen's College Dundee
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.

This paper is an appendix to a joint paper with Professor Macbeath. In (3), it was proved that the invariant measure, m(k), of the set of real n × nmatrices τ, with determinant 1 and norm satisfying ∥τ∥≦ k, had the property that

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

REFERENCES

(1) Dantzig, G. B., Linear Programming and Extensions (Princeton, 1963).Google Scholar
(2) Jack, H., An integral over the interior of a simplex, Proc. Edinburgh Math. Soc. (2) 13 (1962), 167171.CrossRefGoogle Scholar
(3) Jack, H. and Macbeath, A. M., The volume of a certain set of matrices, Proc. Cambridge Phil. Soc. 55 (1959), 213223.CrossRefGoogle Scholar
(4) Macbeath, A. M. and Rogers, C. A., A modified form of Siegel's mean value theorem, Proc. Cambridge Phil. Soc. 51 (1955), 565576.CrossRefGoogle Scholar
(5) Macbeath, A. M. and Rogers, C. A., A modified form of Siegel's mean value theorem II, Proc. Cambridge Phil. Soc. 54 (1958), 322326.CrossRefGoogle Scholar
(6) Macbeath, A. M., On the measure of product sets in a topological group, Jour. London Math. Soc. 35 (1960), 403407.CrossRefGoogle Scholar