This new, modernized edition provides a clear and thorough introduction to matrix computations,a key component of scientific computing Retaining the accessible and hands-on style of its predecessor, Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work. Along with new and updated examples, the Third Edition features: * A novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm * Application of classical Gram-Schmidt with reorthogonalization * A revised approach to the derivation of the Golub-Reinsch SVD algorithm * New coverage on solving product eigenvalue problems * Expanded treatment of the Jacobi-Davidson method * A new discussion on stopping criteria for iterative