Advanced topics

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( 13 )

259 pages

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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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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.

- Self Adjoint Operators
- Simultaneous Diagonalization
- Schur’s Theorem
- Spectral Theory Of Self Adjoint Operators
- Positive And Negative Linear Transformations
- Fractional Powers
- Polar Decompositions
- An Application To Statistics
- The Singular Value Decomposition
- Approximation In The Frobenius Norm
- Least Squares And Singular Value Decomposition
- The Moore Penrose Inverse
- Exercises

- Norms For Finite Dimensional Vector Spaces
- The p Norms
- The Condition Number
- The Spectral Radius
- Series And Sequences Of Linear Operators
- Iterative Methods For Linear Systems
- Theory Of Convergence
- Exercises

- Numerical Methods For Finding Eigenvalues
- The Power Method For Eigenvalues
- The QR Algorithm
- Exercises

- Positive Matrices
- Functions Of Matrices
- Differential Equations
- Compactness And Completeness
- Fundamental Theorem Of Algebra
- Fields And Field Extensions
- Bibliography
- SelectedExercises

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

1. mai 2015 kl. 12.22