Linear Algebra III

Advanced topics

Vurderinger:
( 13 )
143 pages
Sprog:
 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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Om forfatteren

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. Norms
    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
  2. Numerical Methods, Eigenvalues
    1. The Power Method For Eigenvalues
    2. The QR Algorithm
    3. Exercises
  3. Matrix Calculator On The Web
    1. Use Of Matrix Calculator On Web
  4. Positive Matrices
  5. Functions Of Matrices
  6. Differential Equations
    1. Theory Of Ordinary Differential Equations
    2. Linear Systems
    3. Local Solutions
    4. First Order Linear Systems
    5. Geometric Theory Of Autonomous Systems
    6. General Geometric Theory
    7. The Stable Manifold
  7. Compactness And Completeness
    1. The Nested Interval Lemma
    2. Convergent Sequences, Sequential Compactness
  8. Some Topics Flavored With Linear Algebra
    1. The Symmetric Polynomial Theorem
    2. The Fundamental Theorem Of Algebra
    3. Transcendental Numbers
    4. More On Algebraic Field Extensions
  • Bibliography
  • Index

A comprehensive and highly appreciable book for those who think free stuff is not useful. Thanks a lot to the learned author.
1. maj 2015 kl. 12.22
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