Geodesic
Two Problems of the Theory of Quadratic Maps
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 81-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{FAA_2012_46_3_a5,
     author = {A. V. Arutyunov},
     title = {Two {Problems} of the {Theory} of {Quadratic} {Maps}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {81--84},
     year = {2012},
     volume = {46},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a5/}
}
TY  - JOUR
AU  - A. V. Arutyunov
TI  - Two Problems of the Theory of Quadratic Maps
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2012
SP  - 81
EP  - 84
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a5/
LA  - ru
ID  - FAA_2012_46_3_a5
ER  - 
%0 Journal Article
%A A. V. Arutyunov
%T Two Problems of the Theory of Quadratic Maps
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2012
%P 81-84
%V 46
%N 3
%U http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a5/
%G ru
%F FAA_2012_46_3_a5
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/

[1] J.-B. Hiriart-Urruty, SIAM Review, 49:2 (2007), 255–273 | DOI | MR | Zbl

[2] A. V. Arutyunov, Matem. zametki, 84:2 (2008), 163–174 | DOI | MR | Zbl

[3] A. V. Arutyunov, Usloviya ekstremuma. Anormalnye i vyrozhdennye zadachi, Faktorial, M., 1997 | MR | Zbl