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Dilations, linear matrix inequalities, the matrix cube problem, and beta distributions /
An operator C on a Hilbert space \mathcal H dilates to an operator T on a Hilbert space \mathcal K if there is an isometry V:\mathcal H\to \mathcal K such that C= V^* TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor \vartheta (d), expresse...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1232. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 0 | 0 | |a Dilations, linear matrix inequalities, the matrix cube problem, and beta distributions / |c J. William Helton [and three others]. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c 2019. | |
| 264 | 4 | |c ©2019 | |
| 300 | |a 1 online resource (v, 106 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 1947-6221 ; |v volume 257, number 1232 | |
| 500 | |a "January 2019, volume 257, number 1232 (second of 6 numbers)." | ||
| 500 | |a "Keywords:Dilation, completely positive map, linear matrix inequality, spectrahedron, free spectrahedron, matrix cube problem, binomial distribution, beta distribution, robust stability, free analysis"--Online information | ||
| 504 | |a Includes bibliographical references (pages 101-104 and index. | ||
| 505 | 0 | |a Introduction -- Dilations and Free Spectrahedral Inclusions -- Lifting and Averaging -- A Simplified Form for $\vartheta $ -- $\th $ is the Optimal Bound -- The Optimality Condition $\myal =\mybe $ inTerms of Beta Functions -- Rank versus Size for the Matrix Cube -- Free Spectrahedral Inclusion Generalities -- Reformulation of the Optimization Problem -- Simmons' Theorem for Half Integers -- Bounds on the Median and the Equipoint of the Beta Distribution -- Proof of Theorem 1.2 -- Estimating $\th (d)$ for Odd $d$ -- Dilations and Inclusions of Balls -- Probabilistic Theorems and Interpretations Continued | |
| 588 | 0 | |a Print version record. | |
| 520 | |a An operator C on a Hilbert space \mathcal H dilates to an operator T on a Hilbert space \mathcal K if there is an isometry V:\mathcal H\to \mathcal K such that C= V^* TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor \vartheta (d), expressed as a ratio of \Gamma functions for d even, of all d\times d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Matrices. | |
| 650 | 0 | |a Matrix inequalities. | |
| 650 | 6 | |a Matrices. | |
| 650 | 6 | |a Inégalités matricielles. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 0 | 7 | |a Matrices |2 embucm |
| 650 | 7 | |a Matrices |2 fast | |
| 650 | 7 | |a Matrix inequalities |2 fast | |
| 700 | 1 | |a Helton, J. William, |d 1944- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjDk3YMFFPDbdXYfkrV9Qm | |
| 758 | |i has work: |a Dilations, linear matrix inequalities, the matrix cube problem and beta distributions (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGTYKGFKVmpjmfwvCGDvf3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t Dilations, linear matrix inequalities, the matrix cube problem, and beta distributions. |x 0065-9266 |z 9781470434557 |w (DLC) 2018053280 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1232. |x 1947-6221 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5725358 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445226 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5725358 | ||
| 938 | |a EBSCOhost |b EBSC |n 2042356 | ||
| 938 | |a YBP Library Services |b YANK |n 16094607 | ||
| 994 | |a 92 |b IZTAP | ||