Matrix Mathematics (eBook)

Theory, Facts, and Formulas - Second Edition

Dennis S. Bernstein (Autor)

eBook Download: EPUB

2009 | 2., Second Edition
1184 Seiten
Princeton University Press (Verlag)
978-1-4008-3334-4 (ISBN)

Infos

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing

Autor

Dennis S. Bernstein is professor of aerospace engineering at the University of Michigan.

Produkt-Details

• Zusatzinfo: 4 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik
• Schlagworte: absolute value • Addition • Adjugate matrix • Affine hull • Affine space • Big O notation • Block Matrix • canonical form • Characteristic Polynomial • Codomain • coefficient • complex number • Conjugate transpose • Connectivity (graph theory) • Contradiction • Control Theory • Convex cone • convex hull • convex set • corollary • Determinant • Diagonalization • Diagonal matrix • Division by zero • Edition (book) • Eigenvalues and Eigenvectors • Elementary matrix • Engineering • equivalence relation • existential quantification • exponential function • Function (mathematics) • Group (mathematics) • Hadamard product (matrices) • Hamiltonian path • Hermitian matrix • idempotent matrix • Identity matrix • imaginary number • Integer • Inverse element • Invertible matrix • Involutory matrix • Jordan normal form • Kronecker Product • Left inverse • linear algebra • linear differential equation • logarithm • Logical disjunction • Lyapunov stability • Matrix Calculus • Matrix decomposition • matrix exponential • matrix multiplication • matrix norm • matrix representation • multiset • Natural number • Nilpotent matrix • Notation • observability • Open problem • Parameter • partially ordered set • Permutation • Permutation Matrix • polynomial • polynomial matrix • Positive-definite matrix • Positive semidefinite • Proper transfer function • Quadrilateral • Quantity • rational function • real number • Riccati Equation • Right inverse • Schatten norm • scientific notation • singular value decomposition • Skew-symmetric matrix • Special case • Square matrix • Stability Theory • State Space • Strongly connected component • Subset • Surjective function • Symmetric graph • Theorem • Transfer Function • Transfinite number • transformation matrix • Triangular Matrix • Tuple • Unimodular matrix • Unitary matrix • Upper and lower bounds • Writing
• ISBN-10: 1-4008-3334-5 / 1400833345
• ISBN-13: 978-1-4008-3334-4 / 9781400833344