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A simple proof of the Fisher–Fuller theorem

Published online by Cambridge University Press:  24 October 2008

Franklin M. Fisher
Franklin M. Fisher
Affiliation:
Department of EconomicsMassachusetts Institute of Technology
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Extract

Several years ago, Fisher and Fuller(1) proved that if P is a real square matrix with all members of its ‘nested set’ of principal minors non-zero, then there exists a real diagonal matrix, D, such that the characteristic roots of DP are all real, negative and distinct. This interesting and powerful result, used by the authors to derive further results concerning convergence of linear iterative processes, has since also proved of interest to economists studying the stability of economic general equilibrium.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 3 , May 1972 , pp. 523 - 525
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Fisher, M. E. and Fuller, A. T.On the stabilization of matrices and the convergence of linear iterative processes. Proc. Cambridge Philos. Soc. 54 (1958), 417–425.CrossRefGoogle Scholar
(2)McFadden, D. On Hicksian Stability, Chapter 14 of Wolfe, J. N., ed. Value, capital and growth: papers in honour of Sir John Hicks (Edinburgh: Edinburgh University Press, 1968).Google Scholar
(3)Newman, P.Some notes on stability conditions. Review of Economic Studies 27 (1959–1960), 1–9.Google Scholar