Include index.

This book provides comprehensive coverage of matrix theory from a geometric and physical perspective, and the authors address the functionality of matrices and their ability to illustrate and aid in many practical applications. Readers are introduced to inverses and eigenvalues through physical examples such as rotations, reflections, and projections, and only then are computational details described and explored. MATLAB is utilized to aid in reader comprehension, and the authors are careful to address the issue of rank fragility so readers are not flummoxed when MATLAB displays conflict with manual calculations. Matrix foundations are exphasized via projects involving LU factorizations and the matrix aspects of finite difference modeling and Kirchhoff's circuit laws. Vector space concepts and the many facets of orthogonality are then discussed, and in an effort maintain a computational perpective, attention is directed to the numerical issues of error control through norm preservation. Projects include rotational kinematics, Householder implementation of QR factorizations, and the infinite dimensional matrices arising in Haar wavelet formulations. The statistical unlikeliness of singular square matrices, multiple eignevalues, and defective matrices are then emphasized for random matrices, and the basic workings of the QR algorithm (and the role of luck in its implementation as well as in the occurrence of defective matrices) and the random-shift amelioration of its failures are explored. The book concludes with a chapter on the role of matrices in the solution of linear systems of diffential equations (DEs) with constant coefficients via the matrix exponential.