Représentations déterminantales effectives des polynômes univariés par les matrices flèches

2008/09/04 by Ronan Quarez, Quarez, Ronan
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #math.RA

paper · pdf · doi:10.48550/arxiv.0809.0804

arxiv created 2008/09/04 · arxiv updated 2009/12/01

Abstract

We first show the existence of an effective determinantal representation for any univariate polynomial with real coefficients. Then, we more precisely establish that any univariate polynomial with real coefficients has an effective determinantal representation with signature (r+s,s) if and only if it has at least r real roots with multiplicity. The effective determinantal representations we construct used arrow matrices.

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