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A reduction theorem for totally positive matrices. (English) Zbl 0049.17104


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[1] Schoenberg, I. J., Ueber variationsvermindernde lineare Transformationen, Math. Zeitschrift, 32, 321-328 (1930) · JFM 56.0106.06 · doi:10.1007/BF01194637
[2] M. Aissen, I. J. Schoenberg and A. M. Whitney, On the generating functions of totally positive sequences I, this Journal, p. 93. · Zbl 0049.17201
[3] See G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, vol. 2, Problem 76, page 49. Our matrix (2) differs only by positive row and column factors from the matrix ‖q^−2ij‖ whose strict total positivity is implied, by Pólya’s result.
[4] Fekete, M., Ueber ein Problem von Laguerre, Rendiconti del Circolo Matematico di Palermo, 34, 92-93 (1912)
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