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Author: Edward Barry Saff
Publisher: John Wiley & Sons
ISBN: 1118953657
Category : Mathematics
Languages : en
Pages : 407
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Book Description
An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.
Author: Edward Barry Saff
Publisher: John Wiley & Sons
ISBN: 1118953657
Category : Mathematics
Languages : en
Pages : 407
Get Book Here
Book Description
An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.
Author: Fumio Hiai
Publisher: Springer Science & Business Media
ISBN: 3319041509
Category : Mathematics
Languages : en
Pages : 337
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Book Description
Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Author: Xian-Da Zhang
Publisher: Cambridge University Press
ISBN: 1108417418
Category : Computers
Languages : en
Pages : 761
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Book Description
The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.
Author: Edward Barry Saff
Publisher: John Wiley & Sons
ISBN: 1118953681
Category : Mathematics
Languages : en
Pages : 408
Get Book Here
Book Description
An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.
Author: Zhong-Zhi Bai
Publisher: SIAM
ISBN: 1611976634
Category : Mathematics
Languages : en
Pages : 496
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Book Description
This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics
Author: Qi-Ming He
Publisher: Springer Science & Business Media
ISBN: 1461473306
Category : Computers
Languages : en
Pages : 363
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Book Description
Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions. New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.
Author: Fuzhen Zhang
Publisher: Springer Science & Business Media
ISBN: 1475757972
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The only prerequisites are a decent background in elementary linear algebra and calculus.
Author: David S. Watkins
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 476
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Book Description
The use of numerical methods continues to expand rapidly. At their heart lie matrix computations. Written in a clear, expository style, it allows students and professionals to build confidence in themselves by putting the theory behind matrix computations into practice instantly. Algorithms that allow students to work examples and write programs introduce each chapter. The book then moves on to discuss more complicated theoretical material. Using a step-by-step approach, it introduces mathematical material only as it is needed. Exercises range from routine computations and verifications to extensive programming projects and challenging proofs.
Author: Alan J. Laub
Publisher: SIAM
ISBN: 1611972205
Category : Mathematics
Languages : en
Pages : 159
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Book Description
This text provides an introduction to numerical linear algebra together with its application to solving problems arising in state-space control and systems theory. The book provides a number of elements designed to help the reader learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis and an introduction to finite (IEEE) arithmetic, alongside discussion of mathematical software topics. In addition to the fundamental concepts, the text covers statistical condition estimation and gives an overview of certain computational problems in control and systems theory. Engineers and scientists will find this text valuable as a theoretical resource to complement their work in algorithms. For graduate students beginning their study, or advanced undergraduates, this text is ideal as a one-semester course in numerical linear algebra and is a natural follow-on to the author's previous book, Matrix Analysis for Scientists and Engineers.
Author: Sudipto Banerjee
Publisher: CRC Press
ISBN: 1420095382
Category : Mathematics
Languages : en
Pages : 586
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Book Description
Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
