Special matrices of mathematical physics : stochastic, circulant and bell matrices
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Bibliographic Information
Special matrices of mathematical physics : stochastic, circulant and bell matrices
World Scientific, c2001
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Includes bibliographical references and index
Description and Table of Contents
Description
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas concerning Lie algebra invariants, differential geometry and real gases, and their matrices are instrumental in the study of chaotic mappings.
Table of Contents
- Basics: Some Fundamental Notions
- Stochastic Matrices: Evolving Systems
- Markov Chains
- Glass Transition
- The Kerner Model
- Formal Developments
- Equilibrium, Dissipation and Ergodicity
- Circulant Matrices: Prelude
- Definition and Main Properties
- Discrete Quantum Mechanics
- Quantum Symplectic Structure
- Bell Matrices: An Organizing Tool
- Bell Polynomials
- Determinants and Traces
- Projectors and Iterates
- Gases: Real and Ideal.
by "Nielsen BookData"