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049 _aMAIN
100 1 _aFallat, Shaun M.
_963882
245 1 0 _aTotally nonnegative matrices /
_cShaun M. Fallat, Charles R. Johnson.
260 _aPrinceton :
_bPrinceton University Press,
_c�2011.
300 _a1 online resource (248 pages) :
_billustrations
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aPrinceton series in applied mathematics
520 _a"Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references"--
_cProvided by publisher.
520 _a""Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems"--
_cProvided by publisher.
504 _aIncludes bibliographical references (pages 219-238) and index.
588 0 _aPrint version record.
505 0 _aTotally Nonnegative Matrices; Contents; List of Figures; Preface; Chapter 0. Introduction; Chapter 1. Preliminary Results and Discussion; Chapter 2. Bidiagonal Factorization; Chapter 3. Recognition; Chapter 4. Sign Variation of Vectors and TN Linear Transformations; Chapter 5. The Spectral Structure of TN Matrices; Chapter 6. Determinantal Inequalities for TN Matrices; Chapter 7. Row and Column Inclusion and the Distribution of Rank; Chapter 8. Hadamard Products and Powers of TN Matrices; Chapter 9. Extensions and Completions; Chapter 10. Other Related Topics on TN Matrices; Bibliography.
546 _aIn English.
590 _aIEEE
_bIEEE Xplore Princeton University Press eBooks Library
650 0 _aNon-negative matrices.
_963883
650 6 _aMatrices non-n�egatives.
_963884
650 7 _aMATHEMATICS
_xApplied.
_2bisacsh
_95811
650 7 _aMATHEMATICS
_xMatrices.
_2bisacsh
_963672
650 7 _aMATHEMATICS
_xAlgebra
_xLinear.
_2bisacsh
_963885
650 7 _aNon-negative matrices.
_2fast
_0(OCoLC)fst01038561
_963883
655 0 _aElectronic books.
_93294
655 4 _aElectronic books.
_93294
700 1 _aJohnson, Charles R.
_963886
776 0 8 _iPrint version:
_aFallat, Shaun M.
_tTotally nonnegative matrices.
_dPrinceton : Princeton University Press, 2011
_z9780691121574
_w(DLC) 2010052042
_w(OCoLC)679940604
830 0 _aPrinceton series in applied mathematics.
_963887
856 4 0 _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452359
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