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Invariant Subspaces of Matrices with Applications 2nd Edition by Israel Gohberg, Peter Lancaster, Leiba Rodman 089871608X 9780898716085

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Invariant Subspaces of Matrices with Applications 2nd Edition Israel Gohberg Digital Instant Download

Author(s): Israel Gohberg, Peter Lancaster, Leiba Rodman
ISBN(s): 9780898716085, 089871608X
Edition: 2nd
File Details: PDF, 69.60 MB
Year: 2006
Language: english
SKU: EB-1526892 Category: Tags: , ,

Invariant Subspaces of Matrices with Applications 2nd Edition by Israel Gohberg, Peter Lancaster, Leiba Rodman – Ebook PDF Instant Download/Delivery: 089871608X, 978-0898716085
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Product details:

ISBN 10:         089871608X
ISBN 13: 978-0898716085
Author:          Israel Gohberg, Peter Lancaster, Leiba Rodman

This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions.
 

Invariant Subspaces of Matrices with Applications 2nd Table of contents:

1. Introduction
1.1. Linear Operators and Matrices
1.2. Invariant Subspaces
1.3. Applications of Invariant Subspaces

2. Basic Concepts and Results
2.1. Eigenvalues and Eigenvectors
2.2. The Characteristic Polynomial
2.3. Minimal Polynomial
2.4. Diagonalizable Matrices
2.5. Jordan Canonical Form

3. Invariant Subspaces of Matrices
3.1. General Theory of Invariant Subspaces
3.2. Eigenspaces and Generalized Eigenspaces
3.3. Direct Sum Decompositions
3.4. Examples and Applications

4. Orthogonal and Symmetric Matrices
4.1. Symmetric Matrices
4.2. Orthogonal Matrices
4.3. Spectral Theorem for Symmetric Matrices
4.4. Applications to Quadratic Forms

5. The Schur Decomposition and Its Applications
5.1. Schur’s Theorem
5.2. Schur Decomposition in Practice
5.3. Applications to Numerical Methods
5.4. Applications to Control Theory

6. Eigenvalue Sensitivity and Perturbation Theory
6.1. Eigenvalue Sensitivity
6.2. Matrix Perturbation Theory
6.3. Applications to Numerical Analysis
6.4. Applications to System Stability

7. Invariant Subspaces in Dynamical Systems
7.1. Invariant Subspaces in Linear Systems
7.2. Applications to Stability Analysis
7.3. Lyapunov Functions and Invariant Subspaces
7.4. Invariant Subspaces in Control Theory

8. Applications in Quantum Mechanics
8.1. Quantum States and Operators
8.2. Applications of Invariant Subspaces in Quantum Mechanics
8.3. Quantum Measurements and Projections
8.4. Quantum Computation and Invariant Subspaces

9. Singular Value Decomposition and Its Applications
9.1. Singular Value Decomposition (SVD)
9.2. SVD and Low-Rank Approximations
9.3. Applications to Data Analysis and Signal Processing
9.4. Applications in Optimization

10. The Matrix Exponential and Its Applications
10.1. The Matrix Exponential
10.2. Applications to Solving Linear Differential Equations
10.3. Applications to Stability in Dynamical Systems
10.4. Applications to Control Systems

11. Conclusion
11.1. Summary of Key Results
11.2. Further Directions for Research

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