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A Generalization of Cauchy' s Double Alternant

Published online by Cambridge University Press:  20 November 2018

David Carlson  and
Chandler Davis
David Carlson
Affiliation:
University of Wisconsin, University of Toronto
Chandler Davis
Affiliation:
University of Wisconsin, University of Toronto
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The subject of alternants and alternating functions was widely studied during the last century (cf. Muir [6]). One of the best-known alternants is actually a double alternant (rows and columns) defined by Cauchy [2] in 1841. Cauchy's result may be stated as follows:If D = [dpq] p, q = l, …, n, where dpq = (xp+yq)-1, then

1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 273 - 278
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Carlson, David, Rank and inertia theorems for matrices, the semi-definite case, Ph.D. thesis, University of Wisconsin, Madison, Wisconsin, 1963.Google Scholar
2. Cauchy, A., Mémoire sur les fonctions alternées et sur les sommes alternées. Exer. d' analyse et de phys. math.,ii, pp. 151–159 (1841); or Oeuvres complètes Ile série xii.Google Scholar
3. Hahn, Wolfgang, Eine Bemerkung zur zweiten Methode von Lyapunov, Math. Nachrichten, 14 (1955), 349–354.Google Scholar
4. Householder, A.S., Principles of Numerical Analysis, McGraw-Hill, New York, 1953.Google Scholar
5. Marcus, Marvin and Thompson, R.C., The field of values of the Hadamard Product, University of British Columbia, Vancouver, 1962.Google Scholar
6. Muir, Thomas, The Theory of Determinants, Dover, New York, 1960.Google Scholar