Geodesic
A Generalization of Cauchy' s Double Alternant
Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 273-278

Voir la notice de l'article provenant de la source Cambridge University Press

The subject of alternants and alternating functions was widely studiedduring the last century (cf. Muir [6]). One of the best-known alternants isactually a double alternant (rows and columns) defined by Cauchy [2] in1841. Cauchy's result may be stated as follows:If D = [dpq] p, q= l, ..., n, where dpq =(xp+yq)-1, then 1 . 
Carlson, David; Davis, Chandler. A Generalization of Cauchy' s Double Alternant. Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 273-278. doi: 10.4153/CMB-1964-025-8
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[1] 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] 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] 3. Hahn, Wolfgang, Eine Bemerkung zur zweiten Methode von Lyapunov, Math. Nachrichten, 14 (1955), 349–354. Google Scholar

[4] 4. Householder, A.S., Principles of Numerical Analysis, McGraw-Hill, New York, 1953. Google Scholar

[5] 5. Marcus, Marvin and Thompson, R.C., The field of values of the Hadamard Product, University of British Columbia, Vancouver, 1962. Google Scholar

[6] 6. Muir, Thomas, The Theory of Determinants, Dover, New York, 1960. Google Scholar

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