# A Gr\"obner basis proof of the flat extension theorem for moment matrices

@article{Schweighofer2008AGB, title={A Gr\"obner basis proof of the flat extension theorem for moment matrices}, author={M. Schweighofer}, journal={arXiv: Commutative Algebra}, year={2008} }

This paper has been withdrawn by the author since $U$ in Lemma 2 is in general not a subspace.

#### 3 Citations

A Sparse Flat Extension Theorem for Moment Matrices

- Mathematics, Computer Science
- ArXiv
- 2008

This note proves a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices to momentMatrices indexed by an arbitrary set of monomials and its border, when formulated in a basis-free setting. Expand

A generalized flat extension theorem for moment matrices

- Mathematics
- 2009

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow (Memoirs of the American Mathematical Society, vol. 119. American Mathematical Society, Providence, 1996) for… Expand

Sums of Squares, Moment Matrices and Optimization Over Polynomials

- Mathematics
- 2009

We consider the problem of minimizing a polynomial over a semialgebraic set defined by polynomial equations and inequalities, which is NP-hard in general. Hierarchies of semidefinite relaxations have… Expand

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Université de Rennes I, Campus de Beaulieu, 35042 Rennes cedex, France E-mail address: markus.schweighofer@univ-rennes1

- Université de Rennes I, Campus de Beaulieu, 35042 Rennes cedex, France E-mail address: markus.schweighofer@univ-rennes1