AbstractFirst, we show that Sturm algorithm and Sylvester algorithm, which compute the number of real roots of a given univariate polynomial, lead to two dual tridiagonal determinantal representations of the polynomial. Next, we show that the number of real roots of a polynomial given by a tridiagonal determinantal representation is greater than the signature of this representation
We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representati...
Valiant, in his seminal paper in 1979, showed an efficient simulation of algebraic formulas by deter...
A little known property of determinants is developed in a manner accessible to beginning undergradua...
International audienceFirst, we show that Sturm algorithm and Sylvester algorithm, which compute the...
AbstractFirst, we show that Sturm algorithm and Sylvester algorithm, which compute the number of rea...
AbstractWe give an elementary proof, only using linear algebra, of a result due to Helton, Mcculloug...
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-line...
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-line...
For bivariate polynomials of degree $n\le 5$ we give fast numerical constructions of determinantal r...
AbstractThe problem of writing real zero polynomials as determinants of linear matrix polynomials ha...
International audienceWe give an elementary proof, only using linear algebra, of a result due to Hel...
We give two determinantal representations for a bivariate polynomial. They may be used to compute th...
3 figuresInternational audienceThis paper studies Symmetric Determinantal Representations (SDR) in c...
International audienceLet A_0 , A_1 , . . . , A_n be given square matrices of size m with rational c...
Abstract. This paper studies Symmetric Determinantal Representations (SDR) in characteristic 2, that...
We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representati...
Valiant, in his seminal paper in 1979, showed an efficient simulation of algebraic formulas by deter...
A little known property of determinants is developed in a manner accessible to beginning undergradua...
International audienceFirst, we show that Sturm algorithm and Sylvester algorithm, which compute the...
AbstractFirst, we show that Sturm algorithm and Sylvester algorithm, which compute the number of rea...
AbstractWe give an elementary proof, only using linear algebra, of a result due to Helton, Mcculloug...
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-line...
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-line...
For bivariate polynomials of degree $n\le 5$ we give fast numerical constructions of determinantal r...
AbstractThe problem of writing real zero polynomials as determinants of linear matrix polynomials ha...
International audienceWe give an elementary proof, only using linear algebra, of a result due to Hel...
We give two determinantal representations for a bivariate polynomial. They may be used to compute th...
3 figuresInternational audienceThis paper studies Symmetric Determinantal Representations (SDR) in c...
International audienceLet A_0 , A_1 , . . . , A_n be given square matrices of size m with rational c...
Abstract. This paper studies Symmetric Determinantal Representations (SDR) in characteristic 2, that...
We prove a generalization of the Hermitian version of the Helton–Vinnikov determinantal representati...
Valiant, in his seminal paper in 1979, showed an efficient simulation of algebraic formulas by deter...
A little known property of determinants is developed in a manner accessible to beginning undergradua...
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