Determinantal representations of semihyperbolic polynomials
نویسندگان
چکیده
منابع مشابه
Polynomials with and without Determinantal Representations
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 ...
متن کاملNormal and Triangular Determinantal Representations of Multivariate Polynomials
In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form i i i b x a , and in each column the same variable appears. We also apply the algorithm to obtain a triangular determinant representation, a reduced determinant representation, and a uniform determinant representation of any multivariable polynomi...
متن کاملAverage Characteristic Polynomials of Determinantal Point Processes
We investigate the average characteristic polynomial E [∏N i=1(z−xi) ] where the xi’s are real random variables drawn from a Biorthogonal Ensemble, i.e. a determinantal point process associated with a bounded finite-rank projection operator. For a subclass of Biorthogonal Ensembles, which contains Orthogonal Polynomial Ensembles and (mixed-type) Multiple Orthogonal Polynomial Ensembles, we prov...
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...
متن کاملRepresentations of Braid Groups via Determinantal Rings
We construct representations for braid groups Bn via actions of Bn on a determinantal ring, thus mirroring the setting of the classical representation theory for GLn. The representations that we construct fix a certain unitary form.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2016
ISSN: 0026-2285
DOI: 10.1307/mmj/1472066143