Numerical linear algebra with applications : using MATLAB 1. Matrices 2. Linear equations 3. Subspaces 4. Determinants 5. Eigenvalues and eigenvectors 6. Orthogonal vectors and matrices 7. Vector and matrix norms 8. Floating point arithmetic 9. Algorithms 10. Conditioning of problems and stability of algorithms 11. Gaussian elimination and the LU decomposition 12. Linear system applications 13. Important special systems 14. Gram Schmidt orthonormalization 15. The singular value decomposition 16. Least square problems 17. Implementing the QR decomposition 18. The algebraic eigenvalue problem 19. The symmetric eigenvalue problem 20. Basic iterative methods 21. Krylov subspace methods 22. Large sparse eigenvalue problems 23. Computing the singular value decomposition A. Complex numbers B. Mathematical induction C. Chebyshev polynominals Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems Numerical Linear Algebra with Applications contains all the material necessary for a graduate course on numerical linear algebra and numerous applications to engineering and science used in industry. With a unified presentation of computation basic algorithm analysis and numerical methods to compute solutions this book is ideal for solving real world problems. It provides necessary mathematical background information for those who want to learn to solve linear algebra problems using MATLAB and offers a thorough explanation of the issues and methods for practical computation avoiding an extensive theorem proof type of exposition for practical use.