Geodesic
Two Problems of the Theory of Quadratic Maps
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 81-84.

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Given quadratic forms $q_1, \dots, q_k$, 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 $x\ne 0$? Criteria for each of these conditions to hold are obtained. These criteria are stated in terms of matrices determining the quadratic forms under consideration.
Keywords: quadratic form, quadratic map, zero set of a quadratic map. 
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A. V. Arutyunov. Two Problems of the  Theory of Quadratic Maps. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 81-84. http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a5/

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