Abstract
Given quadratic forms q 1, …, q k , two questions are studied: Under what conditions does the set of common zeros of these quadratic forms consist of the only point x = 0? When is the maximum of these quadratic forms nonnegative or positive for any x ≠ 0? Criteria for each of these conditions to hold are obtained. These criteria are stated in terms of matrices determining the quadratic forms under consideration.
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References
J.-B. Hiriart-Urruty, SIAM Review, 49:2 (2007), 255–273.
A. V. Arutyunov, Mat. Zametki, 84:2 (2008), 163–174; English transl.: Math. Notes, 84:1–2 (2008), 155–165.
A. V. Arutyunov, Extremum Conditions. Abnormal and Degenerate Problem [in Russian], Faktorial, Moscow, 1997.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 46, No. 3, pp. 81–84, 2012
Original Russian Text Copyright © by A. V. Arutyunov
This work was financially supported by RFBR grant no. 12-01-00427.
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Arutyunov, A.V. Two problems of the theory of quadratic maps. Funct Anal Its Appl 46, 225–227 (2012). https://doi.org/10.1007/s10688-012-0028-y
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DOI: https://doi.org/10.1007/s10688-012-0028-y