Computing symmetric determinantal representations
نویسندگان
چکیده
منابع مشابه
Symmetric Determinantal Representations in Characteristic 2
This paper studies Symmetric Determinantal Representations (SDR) in characteristic 2, that is the representation of a multivariate polynomial P by a symmetric matrix M such that P = det(M), and where each entry of M is either a constant or a variable. We first give some sufficient conditions for a polynomial to have an SDR. We then give a non-trivial necessary condition, which implies that some...
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The problem of writing real zero polynomials as determinants of linear matrix polynomials has recently attracted a lot of attention. Helton and Vinnikov [9] have proved that any real zero polynomial in two variables has a determinantal representation. Brändén [2] has shown that the result does not extend to arbitrary numbers of variables, disproving the generalized Lax conjecture. We provide a ...
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متن کاملHermitian Determinantal Representations of Hyperbolic Curves
(1) f = det(xM1 + yM2 + zM3), where M1,M2,M3 are Hermitian d × d matrices. The representation is definite if there is a point e ∈ R for which the matrix e1M1+e2M2+e3M3 is positive definite. This imposes an immediate condition on the projective curve VC(f). Because the eigenvalues of a Hermitian matrix are real, every real line passing through e meets this hypersurface in only real points. A pol...
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ژورنال
عنوان ژورنال: Journal of Software for Algebra and Geometry
سال: 2020
ISSN: 1948-7916
DOI: 10.2140/jsag.2020.10.9