, Volume 46, Issue 3, pp 225-227
Date: 14 Sep 2012

Two problems of the theory of quadratic maps

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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.