Fundamentals of Matrix Analysis With Applications

This book provides comprehensive coverage of matrix theory from ageometric and physical perspective, and the authors address thefunctionality of matrices and their ability to illustrate and aidin many practical applications. Readers are introduced toinverses and eigenvalues through physical examples such asrotations, reflections, and projections, and only then arecomputational details described and explored. MATLAB isutilized to aid in reader comprehension, and the authors arecareful to address the issue of rank fragility so readers are notflummoxed when MATLAB displays conflict with manualcalculations. Matrix foundations are exphasized via projectsinvolving LU factorizations and the matrix aspects of finitedifference modeling and Kirchhoff's circuit laws. Vectorspace concepts and the many facets of orthogonality are thendiscussed, and in an effort maintain a computational perpective,attention is directed to the numerical issues of error controlthrough norm preservation. Projects include rotationalkinematics, Householder implementation of QR factorizations, andthe infinite dimensional matrices arising in Haar waveletformulations. The statistical unlikeliness of singular squarematrices, multiple eignevalues, and defective matrices are thenemphasized for random matrices, and the basic workings of the QRalgorithm (and the role of luck in its implementation as well as inthe occurrence of defective matrices) and the random-shiftamelioration of its failures are explored. The book concludeswith a chapter on the role of matrices in the solution of linearsystems of diffential equations (DEs) with constant coefficientsvia the matrix exponential. Insight into the ssues related toits computation are also provided.

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.