Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 225–227 | Cite as

Two problems of the theory of quadratic maps

Brief Communications


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.

Key words

quadratic form quadratic map zero set of a quadratic map 


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  1. [1]
    J.-B. Hiriart-Urruty, SIAM Review, 49:2 (2007), 255–273.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    A. V. Arutyunov, Mat. Zametki, 84:2 (2008), 163–174; English transl.: Math. Notes, 84:1–2 (2008), 155–165.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    A. V. Arutyunov, Extremum Conditions. Abnormal and Degenerate Problem [in Russian], Faktorial, Moscow, 1997.MATHGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Peoples Friendship UniversityMoscowRussia

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