Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)
by Gene H. Golub
from The Johns Hopkins University Press
Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.
Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality
by J. B. Kuipers
from Princeton University Press
Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.
The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.
Schaum's Outline of Theory and Problems of Matrix Operations
by Richard Bronson
from McGraw-Hill
If you want top grades and thorough understanding of matrix operations, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 363 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples, and lack of dreary minutiae, Schaum’s Outlines have sold more than 30 million copies worldwide—and this guide will show you why!
Matrix Analysis
by Roger A. Horn
from Cambridge University Press
Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics.
A presentation of classical as well as recent results of matrix analysis that have proven important to applied mathematics and reflect two concurrent views of the subject.
Matrix and Tensor Calculus: With Applications to Mechanics, Elasticity and Aeronautics
Matrices and Linear Algebra (Dover Books on Advanced Mathematics)
by Hans Schneider
from Dover Publications
Linear Algebra and Matrix Theory
by E. D. Nering
from Wiley
This revision of a well-known text includes more sophisticated mathematical material. A new section on applications provides an introduction to the modern treatment of calculus of several variables, and the concept of duality receives expanded coverage. Notations have been changed to correspond to more current usage.
Matrix Algebra: An Introduction (Quantitative Applications in the Social Sciences)
by Krishnan Namboodiri
from Sage Publications, Inc
Defines basic terms and elementary matrices manipulation, introduces the concept of linear dependence, and explains eigenvalues and eigenvectors with illustrated examples.
Matrix Groups for Undergraduates (Student Mathematical Library,) (Student Mathematical Library)
by Kristopher Tapp
from American Mathematical Society
Matrix groups are a beautiful subject and are central to many fields in mathematics and physics. They touch upon an enormous spectrum within the mathematical arena. This textbook brings them into the undergraduate curriculum. It is excellent for a one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori. The volume is suitable for graduate students and researchers interested in group theory.
Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
by Dennis S. Bernstein
from Princeton University Press
Matrix Mathematics is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application.
Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory.
A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive index are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.
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