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Journal article
A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem
The American mathematical monthly, v 126(7), pp 620-627
09 Aug 2019
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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Details
- Title
- A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem
- Creators
- Anatolii Grinshpan - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- The American mathematical monthly, v 126(7), pp 620-627
- Publisher
- Taylor & Francis
- Number of pages
- 8
- Grant note
- 355645 / Simons Foundation
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000475392500004
- Scopus ID
- 2-s2.0-85068759323
- Other Identifier
- 991019168172804721
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- Web of Science research areas
- Mathematics