Two problems of the theory of quadratic maps
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- Arutyunov, A.V. Funct Anal Its Appl (2012) 46: 225. doi:10.1007/s10688-012-0028-y
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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.