Linear Algebra III

Advanced topics

kirjoittanut Kenneth Kuttler
:
( 13 )
259 pages
Kieli:
 English
This contains advanced topics such as various factorizations, singular value decompositions, Moore Penrose inverse, convergence theorems, and an introduction to numerical methods like QR algorithm.
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Kenneth Kuttler received his Ph.D. in mathematics from The University of Texas at Austin in 1981. From there, he went to Michigan Tech. University where he was employed for most of the next 17 years. He joined the faculty of Brigham Young University in 1998 and has been there since this time. Kuttler'...

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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. This includes more on general fields and an introduction to geometric theory of differential equations. Also it has a short section containing worked exercises from the book.

  1. Self Adjoint Operators
    1. Simultaneous Diagonalization
    2. Schur’s Theorem
    3. Spectral Theory Of Self Adjoint Operators
    4. Positive And Negative Linear Transformations
    5. Fractional Powers
    6. Polar Decompositions
    7. An Application To Statistics
    8. The Singular Value Decomposition
    9. Approximation In The Frobenius Norm
    10. Least Squares And Singular Value Decomposition
    11. The Moore Penrose Inverse
    12. Exercises
  2. Norms For Finite Dimensional Vector Spaces
    1. The p Norms
    2. The Condition Number
    3. The Spectral Radius
    4. Series And Sequences Of Linear Operators
    5. Iterative Methods For Linear Systems
    6. Theory Of Convergence
    7. Exercises
  3. Numerical Methods For Finding Eigenvalues
    1. The Power Method For Eigenvalues
    2. The QR Algorithm
    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
A comprehensive and highly appreciable book for those who think free stuff is not useful. Thanks a lot to the learned author.
1. toukokuuta 2015 klo 12.22
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