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Concerning totally positive matrices see I. J. Schoenberg, Ueber variationsvermindernde lineare Transformationen,Math. Zeitschrift,32 (1930), 321–328, and F. Grantmakher and M. Krein, Sur les matrices complètement non-négatives et oscillatoires,Compositio Math., 4 (1937), 445–476.
M. Aissen, I. J. Schoenberg and A. M. Whitney, On the generating functions of totally positive sequences I, this Journal, p. 93.
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.
M. Fekete, Ueber ein Problem von Laguerre,Rendiconti del Circolo Matematico di Palermo, 34 (1912) pp. 92–93.
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This note is part of a research project sponsored by the Office of Naval Research at the University of Pennsylvania.
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Whitney, A.M. A reduction theorem for totally positive matrices. J. Anal. Math. 2, 88–92 (1952). https://doi.org/10.1007/BF02786969
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DOI: https://doi.org/10.1007/BF02786969