05361nam 2201201 a 450 991079008790332120220311032744.01-283-10154-897866131015491-4008-4059-710.1515/9781400840595(CKB)2670000000083392(EBL)689361(OCoLC)732028359(SSID)ssj0000524103(PQKBManifestationID)11347781(PQKBTitleCode)TC0000524103(PQKBWorkID)10545663(PQKB)10422569(MiAaPQ)EBC689361(StDuBDS)EDZ0000515069(WaSeSS)Ind00023651(DE-B1597)446739(OCoLC)979968553(DE-B1597)9781400840595(Au-PeEL)EBL689361(CaPaEBR)ebr10468682(CaONFJC)MIL310154(PPN)199244944(PPN)187958408(EXLCZ)99267000000008339220110201d2011 uy 0engurnn#---|u||utxtccrMatrix completions, moments, and sums of hermitian squares[electronic resource] /Mihály Bakonyi and Hugo J. WoerdemanCourse BookPrinceton, N.J. Princeton University Press20111 online resource (533 p.)Princeton series in applied mathematicsDescription based upon print version of record.0-691-12889-8 Includes bibliographical references and indexes.Front matter --Contents --Preface --Chapter 1. Cones of Hermitian matrices and trigonometric polynomials --Chapter 2. Completions of positive semidefinite operator matrices --Chapter 3. Multivariable moments and sums of Hermitian squares --Chapter 4. Contractive analogs --Chapter 5. Hermitian and related completion problems --Bibliography --Subject Index --Notation IndexIntensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.Princeton series in applied mathematics.MatricesBernstein–Szeg ő measures.Carathéodory problem.Christoel–Darboux formulas.Corona problem.Fejér–Riesz factorization.Hamburger problem.Hermitian matrices.Hermitian matrix expressions.Hermitian squares problems.Hilbert spaces.Hilbert–Schmidt norm control.MATLAB codes.Nehari problem.Nevanlinna–Pick problem.Schur complement.Toeplitz case.Toeplitz matrices.banded case.chordal case.completion problems.complex function theory.cones.contractive completions.control theory.electrical engineering.linear algebra.mathematics.measure theory.minimal rank completions.multivariables.operator theory.partial operator matrices.positive Carathéodory interpolation.positive definite completions.positive semidefinite completion.quantum information.semidefinite completions.semidefinite matrices.semidefinite operator matrices.semidefinite programming.separability problem.signal processing.trigonometric polynomials.Matrices.512.9434Bakonyi Mihály350649Woerdeman Hugo J1511092MiAaPQMiAaPQMiAaPQBOOK9910790087903321Matrix completions, moments, and sums of hermitian squares3744135UNINA