Représentations déterminantales effectives des polynômes univariés par les matrices flèches

Details Représentations déterminantales effectives des polynômes univariés par les matrices flèches Représentations déterminantales effectives des polynômes univariés par les matrices flèches

2008-09-04

arxiv.org/abs/0809.0804v1

Mathematics

Rings and Algebras

Scientific paper

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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