Special Matrices Of Mathematical Physics: Stochastic, Circulant And Bell MatricesWorld Scientific, 2001 M08 17 - 340 páginas 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. |
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Página viii
... matrices whose entries are themselves matrices . A matrix symplectic structure comes out in a natural way and sheds new light on the underlying texture of phase space . Bell polynomials , and the matrices of which they are the entries ...
... matrices whose entries are themselves matrices . A matrix symplectic structure comes out in a natural way and sheds new light on the underlying texture of phase space . Bell polynomials , and the matrices of which they are the entries ...
Página ix
Ruben Aldrovandi. reduced to matrix multiplication . In particular , the map iterations describ- ing discrete - time dynamical systems become powers of matrices ... Bell polynomials in the variables f1 , f2 , ... , fn - k + 1 · The author ...
Ruben Aldrovandi. reduced to matrix multiplication . In particular , the map iterations describ- ing discrete - time dynamical systems become powers of matrices ... Bell polynomials in the variables f1 , f2 , ... , fn - k + 1 · The author ...
Página xi
... matrix 1.3 Matrix functions 1.3.1 Nondegenerate matrices 1.3.2 Degenerate matrices 1.4 Normal matrices STOCHASTIC MATRICES Chapter 2 Evolving systems Chapter 3 Markov chains 3.1 Non - negative matrices 3.2 General properties 3.2.1 Flow ...
... matrix 1.3 Matrix functions 1.3.1 Nondegenerate matrices 1.3.2 Degenerate matrices 1.4 Normal matrices STOCHASTIC MATRICES Chapter 2 Evolving systems Chapter 3 Markov chains 3.1 Non - negative matrices 3.2 General properties 3.2.1 Flow ...
Página xiii
... equation 11.3.3 Quantum tapestry BELL MATRICES Chapter 12 An organizing tool Chapter 13 Bell polynomials 13.1 Definition and elementary properties 13.1.1 Formal examples 149 151 151 157 13.2 The matrix representation . 165 13.2.1 An ...
... equation 11.3.3 Quantum tapestry BELL MATRICES Chapter 12 An organizing tool Chapter 13 Bell polynomials 13.1 Definition and elementary properties 13.1.1 Formal examples 149 151 151 157 13.2 The matrix representation . 165 13.2.1 An ...
Página xv
... Bell matrices A.7.1 Schröder equation A.7.2 Fredholm theory 302 303 303 A.8 Statistical mechanics . 304 A.8.1 Microcanonical ensemble 304 A.8.2 Canonical ensemble 304 A.8.3 Grand canonical ensemble . 305 A.8.4 Ideal relativistic quantum ...
... Bell matrices A.7.1 Schröder equation A.7.2 Fredholm theory 302 303 303 A.8 Statistical mechanics . 304 A.8.1 Microcanonical ensemble 304 A.8.2 Canonical ensemble 304 A.8.3 Grand canonical ensemble . 305 A.8.4 Ideal relativistic quantum ...
Contenido
19 | |
CIRCULANT MATRICES | 79 |
BELL MATRICES | 147 |
Appendix A Formulary | 283 |
Bibliography | 309 |
Index | 315 |
Otras ediciones - Ver todas
Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell ... Ruben Aldrovandi Vista previa limitada - 2001 |
Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell ... Ruben Aldrovandi Vista previa limitada - 2001 |
Términos y frases comunes
alphabet basis Bell matrices Bell polynomials braid group canonical partition function characteristic polynomial circulant matrices circulant matrix classical cluster integrals column commutative components condition consequently continuum convolution corresponding cyclic defined derivative detailed balancing diagonal differential discrete distribution dynamical eigenvalues eigenvectors entries ep+1 equation equilibrium evolution example factor fermions finite formalism formula Fourier transformations Fredholm geometry given glass grand canonical partition Hamiltonian Hopf algebras identity imprimitive invariant inverse irreducible iterate leads Lie algebra Markov chain noncommutative notation obtained operator particles permutation phase space Phys physical Poisson bracket powers projectors properties QN(B Quantum Mechanics recursion representation Statistical Mechanics stochastic matrix summation symmetric functions symmetric group symplectic Taylor coefficients theorem theory totally regular unitary values variables vector virial Weyl-Wigner Wigner functions Σ Σ