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arXiv · 1905.04751

A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem

Anatolii Grinshpan·Hugo J. Woerdeman
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Abstract

Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We give a linear-algebraic approach to Hilbert's theorem by showing that a structured cone of positive semidefinite matrices is generated by rank 1 elements.

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Anatolii Grinshpan, Hugo J. Woerdeman. 2019-05-12. A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem. https://arxiv.org/abs/1905.04751

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