Sums of squares II: matrix functions Article Swipe
Lyudmila Korobenko
,
Eric T. Sawyer
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2107.12505
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2107.12505
This is the second in a series of three papers dealing with sums of squares and hypoellipticity in the infinitely degenerate regime. We give sharp conditions on the entries of a positive semidefinite NxN matrix function F on n-dimensional Euclidean space, whose determinant vanishes only at the origin and such that F is comparable to its diagonal matrix, in order that F is a finite sum of squares of C^2,delta vector fields. We also consider slightly more general decompositions in which a single quasiconformal term need not be a sum of squares.
Related Topics
Concepts
Mathematics
Explained sum of squares
Degenerate energy levels
Matrix (chemical analysis)
Diagonal
Euclidean space
Order (exchange)
Positive-definite matrix
Least-squares function approximation
Combinatorics
Pure mathematics
Function (biology)
Series (stratigraphy)
Diagonal matrix
Mathematical analysis
Eigenvalues and eigenvectors
Statistics
Geometry
Physics
Quantum mechanics
Estimator
Finance
Paleontology
Composite material
Biology
Materials science
Evolutionary biology
Economics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2107.12505
- https://arxiv.org/pdf/2107.12505
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4318566677
All OpenAlex metadata
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https://openalex.org/W4318566677Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2107.12505Digital Object Identifier
- Title
-
Sums of squares II: matrix functionsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-07-26Full publication date if available
- Authors
-
Lyudmila Korobenko, Eric T. SawyerList of authors in order
- Landing page
-
https://arxiv.org/abs/2107.12505Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2107.12505Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2107.12505Direct OA link when available
- Concepts
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Mathematics, Explained sum of squares, Degenerate energy levels, Matrix (chemical analysis), Diagonal, Euclidean space, Order (exchange), Positive-definite matrix, Least-squares function approximation, Combinatorics, Pure mathematics, Function (biology), Series (stratigraphy), Diagonal matrix, Mathematical analysis, Eigenvalues and eigenvectors, Statistics, Geometry, Physics, Quantum mechanics, Estimator, Finance, Paleontology, Composite material, Biology, Materials science, Evolutionary biology, EconomicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.sums | 12 |
| abstract_inverted_index.term | 84 |
| abstract_inverted_index.that | 50, 60 |
| abstract_inverted_index.with | 11 |
| abstract_inverted_index.order | 59 |
| abstract_inverted_index.sharp | 24 |
| abstract_inverted_index.three | 8 |
| abstract_inverted_index.which | 80 |
| abstract_inverted_index.whose | 41 |
| abstract_inverted_index.finite | 64 |
| abstract_inverted_index.matrix | 34 |
| abstract_inverted_index.origin | 47 |
| abstract_inverted_index.papers | 9 |
| abstract_inverted_index.second | 3 |
| abstract_inverted_index.series | 6 |
| abstract_inverted_index.single | 82 |
| abstract_inverted_index.space, | 40 |
| abstract_inverted_index.vector | 70 |
| abstract_inverted_index.dealing | 10 |
| abstract_inverted_index.entries | 28 |
| abstract_inverted_index.fields. | 71 |
| abstract_inverted_index.general | 77 |
| abstract_inverted_index.matrix, | 57 |
| abstract_inverted_index.regime. | 21 |
| abstract_inverted_index.squares | 14, 67 |
| abstract_inverted_index.consider | 74 |
| abstract_inverted_index.diagonal | 56 |
| abstract_inverted_index.function | 35 |
| abstract_inverted_index.positive | 31 |
| abstract_inverted_index.slightly | 75 |
| abstract_inverted_index.squares. | 91 |
| abstract_inverted_index.vanishes | 43 |
| abstract_inverted_index.C^2,delta | 69 |
| abstract_inverted_index.Euclidean | 39 |
| abstract_inverted_index.comparable | 53 |
| abstract_inverted_index.conditions | 25 |
| abstract_inverted_index.degenerate | 20 |
| abstract_inverted_index.infinitely | 19 |
| abstract_inverted_index.determinant | 42 |
| abstract_inverted_index.semidefinite | 32 |
| abstract_inverted_index.n-dimensional | 38 |
| abstract_inverted_index.decompositions | 78 |
| abstract_inverted_index.quasiconformal | 83 |
| abstract_inverted_index.hypoellipticity | 16 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |