Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions. (Record no. 9062)
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| fixed length control field | 04366nam a22004933i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5725358 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113622.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2018 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470449476 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470434557 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5725358 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5725358 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1081124009 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA188 .H458 2019 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.9434 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Helton, J. William. |
| 245 10 - TITLE STATEMENT | |
| Title | Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2018. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (118 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.257 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 15.1. The nature of equipoints -- Bibliography -- Index -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic 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 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Matrices. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Matrix inequalities. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Klep, Igor. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | McCullough, Scott. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Helton, J. William |
| Title | Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2018 |
| International Standard Book Number | 9781470434557 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5725358">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5725358</a> |
| Public note | Click to View |
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