Totally Nonnegative Matrices (eBook)

Shaun M. Fallat, Charles R. Johnson (Autoren)

eBook Download: EPUB

2011
264 Seiten
Princeton University Press (Verlag)
978-1-4008-3901-8 (ISBN)

Infos

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.

Autor

Shaun M. Fallat is professor of mathematics and statistics at the University of Regina. Charles R. Johnson is the Class of 1961 Professor of Mathematics at the College of William & Mary.

Produkt-Details

• Erscheint lt. Verlag: 11.4.2011
• Reihe/Serie: Princeton Series in Applied Mathematics
• Reihe/Serie: Princeton Series in Applied Mathematics
• Zusatzinfo: 21 b/w illus. 3 tables.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik
• Schlagworte: Addition • Adjugate matrix • algorithm • Analysis • Applied mathematics • Approximation • bidiagonal factorization • Bidiagonal matrix • Big O notation • Calculation • Cardinality • Cauchy–Binet formula • Cauchy matrix • Cayley transform • Characteristic Polynomial • Characterization (mathematics) • chordal graph • coefficient • Coefficient matrix • collocation • combinatorics • Complement (set theory) • completions • complex number • Computation • Constructions • Contradiction • convex hull • convex set • core matrix theory • cornelis • corollary • critical exponent • Cumulative distribution function • Descartes' rule of signs • detection • detemrinants • Determinant • determinantal identities • determinantal inequalities • diagonal • Diagonally dominant matrix • Diagonal matrix • diagram • Diagram (category theory) • directed graph • direct sum • direct summation • Dynamical system • EB factorization • eigenvalues • Eigenvalues and Eigenvectors • Eigenvectors • Elementary diagram • elementary linear algebra • empty set • Equation • existential quantification • exponential distribution • Extensions • Factorization • failure rate • Gamma distribution • geometric design • Glossary • Graph (discrete mathematics) • Hadamard core • Hadamard multiplication • Hadamard powers • Hadamard product (matrices) • Hadamard products • Hadamard's inequality • Hankel matrix • Hermitian matrix • humility • Identity matrix • IITN matrices • Inequality (mathematics) • Ingrid Daubechies • Initial Value Problem • Integer • Invertible matrix • Jacobi matrices • Jacobi matrix • Jan Karel Lenstra • Laplace expansion • linear algebra • Linear combination • Linear map • linear transformations • line insertion • LU decomposition • LU factorization • Main diagonal • Majorization • Markov Chain • Mathematical Analysis • Mathematical and theoretical biology • Mathematical Induction • Mathematics • Matrix Completion • Matrix Completion Problems • Matrix decomposition • matrix function • matrix theory • Matrix theory (physics) • Minor (linear algebra) • MLBC graphs • M-matrix • Natural number • Nomenclature • Nonnegative Matrix • nonnegativity • Normal distribution • Notation • Null vector • Numerical analysis • Parameter • partial differential equation • partially ordered set • partial TN matrices • Pascal matrix • Permutation • Permutation Matrix • Perron complements • Perron-Frobenius theory • Piecewise • planar diagrams • P-matrix • polynomial • polynomial matrix • Positive-definite matrix • Positive element • positive minors • Positive semidefinite • positive semidefinite matrices • Positivity • powers • principal minors • Probability density function • Publishing • Quantity • rank deficiency • rank deficient submatrices • Rank (linear algebra) • rate function • real number • Recognition • remainder • Reply (TV series) • result • retractions • Roots • Row and column spaces • Sailing • Schur complement • scientific notation • Semialgebraic set • Semigroup • Sign (mathematics) • sign variation diminution • Simultaneous Equations • singular value decomposition • Special case • spectral properties • spectral radius • Spline (mathematics) • Square matrix • square root • Stable polynomial • Statistic • Statistics • stochastic • subdeterminants • subdirect sums • Subset • Summation • Support (mathematics) • Technology • Terminology • Theorem • theory • thermodynamics • TN completions • TN linear transformations • TN matrices • TN matrix • TN matrix structure • TN perturbations • TN polynomial matrices • Toeplitz Matrix • totally nonnegative matrices • totally positive matrices • Totally positive matrix • Total order • Total Positivity • TP intervals • TP matrices • TP matrix • TP polynomial matrices • transpose • triangular factorization • Triangular Matrix • tridiagonal matrix • Unordered pair • Vandermonde matrices • Vandermonde matrix • Variable (mathematics) • variation diminution • Vectors • Without loss of generality • Zero element • Zero of a function
• ISBN-10: 1-4008-3901-7 / 1400839017
• ISBN-13: 978-1-4008-3901-8 / 9781400839018