Linear Algebra III Advanced topics
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740302424
Table of contents: title: Content; title: 1. Self Adjoint Operators; title: 1.1. Simultaneous Diagonalization; title: 1.2. Schur’s Theorem; title: 1.3. Spectral Theory Of Self Adjoint Operators; title: 1.4. Positive And Negative Linear Transformations; title: 1.5. Fractional Powers; title: 1.6. Polar Decompositions; title: 1.7. An Application To Statistics; title: 1.8. The Singular Value Decomposition; title: 1.9. Approximation In The Frobenius Norm; title: 1.10. Least Squares And Singular Value Decomposition; title: 1.11. The Moore Penrose Inverse; title: 1.12. Exercises; title: 2. Norms For Finite Dimensional Vector Spaces; title: 2.1. The p Norms; title: 2.2. The Condition Number; title: 2.3. The Spectral Radius; title: 2.4. Series And Sequences Of Linear Operators; title: 2.5. Iterative Methods For Linear Systems; title: 2.6. Theory Of Convergence; title: 2.7. Exercises; title: 3. Numerical Methods For Finding Eigenvalues; title: 3.1. The Power Method For Eigenvalues; title: 3.2. The QR Algorithm; title: 3.3. Exercises; title: 4. Positive Matrices; title: 5. Functions Of Matrices; title: 6. Differential Equations; title: 7. Compactness And Completeness; title: 8. Fundamental Theorem Of Algebra; title: 9. Fields And Field Extensions; title: 10. Bibliography; title: 11. SelectedExercises