# Symmetric Determinantal Representation of Formulas and Weakly Skew Circuits

@article{Grenet2010SymmetricDR, title={Symmetric Determinantal Representation of Formulas and Weakly Skew Circuits}, author={Bruno Grenet and Erich L. Kaltofen and Pascal Koiran and Natacha Portier}, journal={ArXiv}, year={2010}, volume={abs/1007.3804} }

We deploy algebraic complexity theoretic techniques for constructing symmetric determinantal representations of formulas and weakly skew circuits. Our representations produce matrices of much smaller dimensions than those given in the convex geometry literature when applied to polynomials having a concise representation (as a sum of monomials, or more generally as an arithmetic formula or a weakly skew circuit). These representations are valid in any field of characteristic different from 2. In…

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