Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- 1 Vector and Matrix Algebra
- 2 Algebraic Eigenproblems and Their Applications
- 3 Differential Eigenproblems and Their Applications
- 4 Vector and Matrix Calculus
- 5 Analysis of Discrete Dynamical Systems
- Part II Numerical Methods
- Part III Least Squares and Optimization
- References
- Index
2 - Algebraic Eigenproblems and Their Applications
from Part I - Matrix Methods
Published online by Cambridge University Press: 18 February 2021
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- 1 Vector and Matrix Algebra
- 2 Algebraic Eigenproblems and Their Applications
- 3 Differential Eigenproblems and Their Applications
- 4 Vector and Matrix Calculus
- 5 Analysis of Discrete Dynamical Systems
- Part II Numerical Methods
- Part III Least Squares and Optimization
- References
- Index
Summary
The algebraic eigenproblem is the mathematical answer to the physical questions:What are the principal stresses in a solid or fluid and on what planes do they act?What are the natural frequencies of a system?Is the system stable to small disturbances?What is the best basis with respect to which to solve a system of linear algebraic equations with a real symmetric coefficient matrix?What is the best basis with respect to which to solve a system of linear ordinary differential equations?What is the best basis with respect to which to represent an experimental or numerical data set?
Keywords
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- Information
- Publisher: Cambridge University PressPrint publication year: 2021