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

Published online by Cambridge University Press:  20 January 2009

Henry Jack
Henry Jack
Affiliation:
Queen's College Dundee
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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
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 3 , June 1967 , pp. 209 - 213
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), 167–171.CrossRefGoogle Scholar
(3) Jack, H. and Macbeath, A. M., The volume of a certain set of matrices, Proc. Cambridge Phil. Soc. 55 (1959), 213–223.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), 565–576.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), 322–326.CrossRefGoogle Scholar
(6) Macbeath, A. M., On the measure of product sets in a topological group, Jour. London Math. Soc. 35 (1960), 403–407.CrossRefGoogle Scholar