Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 225–227

Two problems of the theory of quadratic maps

Brief Communications

DOI: 10.1007/s10688-012-0028-y

Cite this article as:
Arutyunov, A.V. Funct Anal Its Appl (2012) 46: 225. doi:10.1007/s10688-012-0028-y

Abstract

Given quadratic forms q1, …, qk, 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 formquadratic mapzero set of a quadratic map

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Peoples Friendship UniversityMoscowRussia