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006			m o d |
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008			240724s2018 xx o ||||0 eng d
020			_a9781470449476 _q(electronic bk.)
020			_z9781470434557
035			_a(MiAaPQ)EBC5725358
035			_a(Au-PeEL)EBL5725358
035			_a(OCoLC)1081124009
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA188 .H458 2019
082	0		_a512.9434
100	1		_aHelton, J. William.
245	1	0	_aDilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2018.
264		4	_c©2019.
300			_a1 online resource (118 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.257
505	0		_aCover -- Title page -- Chapter 1. Introduction -- 1.1. Simultaneous dilations -- 1.2. Solution of the minimization problem (1.1) -- 1.3. Linear matrix inequalities (LMIs), spectrahedra and general dilations -- 1.4. Interpretation in terms of completely positive maps -- 1.5. Matrix cube problem -- 1.6. Matrix balls -- 1.7. Adapting the Theory to Free Nonsymmetric Variables -- 1.8. Probabilistic theorems and interpretations -- 1.9. Reader's guide -- Chapter 2. Dilations and Free Spectrahedral Inclusions -- Chapter 3. Lifting and Averaging -- Chapter 4. A Simplified Form for -- Chapter 5. þ is the Optimal Bound -- 5.1. Averages over ( ) equal averages over ^{ -1} -- 5.2. Dilating to commuting self-adjoint operators -- 5.3. Optimality of \ka_{*}( ) -- Chapter 6. The Optimality Condition \myal=\mybe inTerms of Beta Functions -- Chapter 7. Rank versus Size for the Matrix Cube -- 7.1. Proof of Theorem 1.6 -- Chapter 8. Free Spectrahedral Inclusion Generalities -- 8.1. A general bound on the inclusion scale -- 8.2. The inclusion scale equals the commutability index -- Chapter 9. Reformulation of the Optimization Problem -- Chapter 10. Simmons' Theorem for Half Integers -- 10.1. The upper boundary case -- 10.2. The lower boundary cases for even -- 10.3. The lower boundary cases for odd -- Chapter 11. Bounds on the Median and the Equipoint of the Beta Distribution -- 11.1. Lower bound for the equipoint \eiha -- 11.2. New bounds on the median of the beta distribution -- Chapter 12. Proof of Theorem 1.2 -- 12.1. An auxiliary function -- Chapter 13. Estimating þ( ) for Odd -- 13.1. Proof of Theorem 13.1 -- 13.2. Explicit bounds on þ( ) -- Chapter 14. Dilations and Inclusions of Balls -- 14.1. The general dilation result -- 14.2. Four types of balls -- 14.3. Inclusions and dilations -- Chapter 15. Probabilistic Theorems and Interpretations Continued.
505	8		_a15.1. The nature of equipoints -- Bibliography -- Index -- Back Cover.
520			_aAn 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.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aMatrices.
650		0	_aMatrix inequalities.
655		4	_aElectronic books.
700	1		_aKlep, Igor.
700	1		_aMcCullough, Scott.
776	0	8	_iPrint version: _aHelton, J. William _tDilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions _dProvidence : American Mathematical Society,c2018 _z9781470434557
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5725358 _zClick to View
999			_c9062 _d9062