Computational problems for vector-valued quadratic forms

Simple item page
dc.creatorBullo, Francesco
dc.creatorCortes, Jorge
dc.creatorLewis, Andrew D.
dc.creatorMartinez, Sonia
dc.date2002-04-05
dc.date.accessioned2026-07-07T04:47:28Z
dc.date.available2026-07-07T04:47:28Z
dc.descriptionGiven two real vector spaces $U$ and $V$, and a symmetric bilinear map $B: U\times U\to V$, let $Q_B$ be its associated quadratic map $Q_B$. The problems we consider are as follows: (i) are there necessary and sufficient conditions, checkable in polynomial-time, for determining when $Q_B$ is surjective?; (ii) if $Q_B$ is surjective, given $v\in V$ is there a polynomial-time algorithm for finding a point $u\in Q_B^{-1}(v)$?; (iii) are there necessary and sufficient conditions, checkable in polynomial-time, for determining when $B$ is indefinite? We present an alternative formulation of the problem of determining the image of a vector-valued quadratic form in terms of the unprojectivised Veronese surface. The relation of these questions with several interesting problems in Control Theory is illustrated.
dc.description6 pages, no figures, submitted to Workshop on Open Problems in Mathematical Systems and Control Theory
dc.identifierhttps://arxiv.org/abs/math/0204068
dc.identifierhttp://arxiv.org/abs/math/0204068
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63725
dc.subjectAlgebraic Geometry
dc.subjectComputational Complexity
dc.subjectOptimization and Control
dc.subject11Exx; 14Pxx; 14Q99; 15A63
dc.titleComputational problems for vector-valued quadratic forms
dc.typetext

Files

Collections

arXiv