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Positivity of the principal minors of a nonsingularM-matrix

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Abstract

One gives an elementary proof of the known fact that if the principal minors of an M -matrix with a positive determinant are nonnegative, then they are positive.

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Literature cited

  1. A. M. Ostrowski, “Über die Determinanten mit überwiegender Hauptdiagonale,” Comment. Math. Helv.,10, 69–96 (1937).

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Authors
  1. V. V. Ishkhanov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 111, p. 88, 1981.

In conclusion, we note that this problem was suggested to the author by V. P. If'in.

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Ishkhanov, V.V. Positivity of the principal minors of a nonsingularM-matrix. J Math Sci 24, 55–56 (1984). https://doi.org/10.1007/BF01230264

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  • DOI: https://doi.org/10.1007/BF01230264

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