Hyperbolic Polynomials and Generalized Clifford Algebras
نویسندگان
چکیده
منابع مشابه
Hyperbolic Polynomials and Generalized Clifford Algebras
We consider the problem of realizing hyperbolicity cones as spectrahedra, i.e. as linear slices of cones of positive semidefinite matrices. The generalized Lax conjecture states that this is always possible. We use generalized Clifford algebras for a new approach to the problem. Our main result is that if −1 is not a sum of hermitian squares in the Clifford algebra of a hyperbolic polynomial, t...
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The representations of Clifford algebras and their involutions and antiinvolutions are fully investigated since decades. However, these representations do sometimes not comply with usual conventions within physics. A few simple examples are presented, which point out that the hyperbolic numbers can close this gap. PACS: 03.65.Fd; 02.20.Sv; 02.40.Tt; 02.40.-k; 04.50.+h MSC: 81R05; 11E88; 51H30; ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2014
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-014-9598-1