Symmetric Determinantal Representation of Polynomials

Ronan Quarez (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We give an elementary proof, only using linear algebra, of a result due to Helton, Mccullough and Vinnikov, which says that any polynomial can be written as the determinant of a symmetric affine linear pencil.

Mots clés: determinantal representation; linear pencil

Domaines: Anneaux et algèbres [math.RA]

Ronan Quarez. Symmetric Determinantal Representation of Polynomials. Linear Algebra and its Applications, 2012, 436 (9), pp.3642-3660. ⟨10.1016/j.laa.2012.01.004⟩. ⟨hal-00275615⟩