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Bounds for determinants with dominant principal diagonal


Author: G. Baley Price
Journal: Proc. Amer. Math. Soc. 2 (1951), 497-502
MSC: Primary 09.0X
DOI: https://doi.org/10.1090/S0002-9939-1951-0041093-2
MathSciNet review: 0041093
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    E. Fischer, Ueber den Hadamardschen Determinantensatz, Archiv der Mathematik und Physik (3) vol. 13 (1908) pp. 32-40. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, 1934. Helge von Koch, Über das Nichtverschwinden einer Determinante nebst Bemerkungen über Systeme unendlich vieler linearer Gleichungen, Jber. Deutschen Math. Verein. vol. 22 (1913) pp. 285-291. Thomas Muir, Contributions to the history of determinants 1900-1920, London, Blackie, 1930. E. J. Nanson, A determinant inequality, Messenger of Mathematics vol. 31 (1901-1902) pp. 48-50. A. Ostrowski, Sur la détermination des bornes inférieures pour une classe des déterminants, Bull. Sci. Math. (2) vol. 61 (1937) pp. 19-32.
  • Alexander Ostrowski, Über die determinanten mit überwiegender Hauptdiagonale, Comment. Math. Helv. 10 (1937), no. 1, 69–96 (German). MR 1509568, DOI https://doi.org/10.1007/BF01214284
  • Otto Szász, Über eine Verallgemeinerung des Hadamardschen Determinantensatzes, Monatsh. Math. Phys. 28 (1917), no. 1, 253–257 (German). MR 1548909, DOI https://doi.org/10.1007/BF01698247
  • Olga Taussky, A recurring theorem on determinants, Amer. Math. Monthly 56 (1949), 672–676. MR 32557, DOI https://doi.org/10.2307/2305561

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Article copyright: © Copyright 1951 American Mathematical Society