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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, 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.
PART I INTRODUCTION: THREE EXAMPLES
1 Systems of Linear Algebraic Equations
2 Matrix Algebra
PART II INTRODUCTION: THE STRUCTURE OF GENERAL SOLUTIONS TO LINEAR ALGEBRAIC EQUATIONS
3 Vector Spaces
PART III INTRODUCTION: REFLECT ON THIS
5 Eigenvectors and Eigenvalues
7 Linear Systems of Differential Equations
Edward Barry Saff :- PhD, is Professor in the Department of Mathematics and Director of the Center for Constructive Approximation at Vanderbilt University. Dr. Saff is an Inaugural Fellow of the American Mathematical Society, Foreign Member of the Bulgarian Academy of Science, and the recipient of both a Guggenheim and Fulbright Fellowship. He is Editor-in-Chief of two research journals, Constructive Approximation and Computational Methods and Function Theory, and has authored or co-authored over 250 journal articles and eight books. Dr. Saff also serves as an organizer for a sequence of international research conferences that help to foster the careers of mathematicians from developing countries. Arthur David Snider :- PhD, is Professor Emeritus at the University of South Florida (USF), where he served on the faculties of the Departments of Mathematics, Physics, and Electrical Engineering. Previously an analyst at the Massachusetts Institute of Technology's Draper Lab and recipient of the USF Krivanek Distinguished Teacher Award, he consults in industry and has authored or co-authored over 100 journal articles and eight books. With the support of National Science Foundation, Dr. Snider also pioneered a course in fine art appreciation for engineers.