An edition of Linear Algebra III Advanced topics
(2013)
Linear Algebra III Advanced topics
by Kenneth Kuttler
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Last edited by Alice Kirk
June 26, 2015 | History
This contains advanced topics such as various factorizations, singular value decompositions, Moore Penrose inverse, norms, convergence theorems, and an introduction to numerical methods like QR algorithm. Finally, there are some appendices which contain applications of linear algebra or linear algebra techniques.
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Publish Date
2013
Publisher
Bookboon.com
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Book Details
Table of Contents
Content
1. Self Adjoint Operators
1.1. Simultaneous Diagonalization
1.2. Schur’s Theorem
1.3. Spectral Theory Of Self Adjoint Operators
1.4. Positive And Negative Linear Transformations
1.5. Fractional Powers
1.6. Polar Decompositions
1.7. An Application To Statistics
1.8. The Singular Value Decomposition
1.9. Approximation In The Frobenius Norm
1.10. Least Squares And Singular Value Decomposition
1.11. The Moore Penrose Inverse
1.12. Exercises
2. Norms For Finite Dimensional Vector Spaces
2.1. The p Norms
2.2. The Condition Number
2.3. The Spectral Radius
2.4. Series And Sequences Of Linear Operators
2.5. Iterative Methods For Linear Systems
2.6. Theory Of Convergence
2.7. Exercises
3. Numerical Methods For Finding Eigenvalues
3.1. The Power Method For Eigenvalues
3.2. The QR Algorithm
3.3. Exercises
4. Positive Matrices
5. Functions Of Matrices
6. Differential Equations
7. Compactness And Completeness
8. Fundamental Theorem Of Algebra
9. Fields And Field Extensions
10. Bibliography
11. SelectedExercises
ID Numbers
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| June 26, 2015 | Edited by Alice Kirk | Edited without comment. |
| June 26, 2015 | Created by Alice Kirk | Added new book. |