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. |
Dentro del libro
Resultados 1-5 de 93
Página viii
... matrices have not much in common , except for the fact that they appear to open new ways to ... matrices are introduced as instruments to describe in a surprisingly simple way dynamical systems of a wide variety of behaviors . Circulants ...
... matrices have not much in common , except for the fact that they appear to open new ways to ... matrices are introduced as instruments to describe in a surprisingly simple way dynamical systems of a wide variety of behaviors . Circulants ...
Página ix
... Matrices , square or not , are indicated by boldface symbols as M , v , etc. , unless that make the notation too charged . In particular , matrix functions of matrices are typed like F ( M ) . Entries , however , are noted in common ...
... Matrices , square or not , are indicated by boldface symbols as M , v , etc. , unless that make the notation too charged . In particular , matrix functions of matrices are typed like F ( M ) . Entries , however , are noted in common ...
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 xii
... CIRCULANT MATRICES Chapter 8 Prelude 81 Chapter 9 Definition and main properties 83 9.1 Bases • 93 9.2 Double Fourier transform 95 9.3 Random walks 96 Chapter 10 Discrete quantum mechanics 10.1 Introduction . 99 99 10.2 Weyl ...
... CIRCULANT MATRICES Chapter 8 Prelude 81 Chapter 9 Definition and main properties 83 9.1 Bases • 93 9.2 Double Fourier transform 95 9.3 Random walks 96 Chapter 10 Discrete quantum mechanics 10.1 Introduction . 99 99 10.2 Weyl ...
Página xiii
... matrix representation . 165 13.2.1 An important inversion formula . 169 13.3 The Lagrange inversion formula . 171 13.3.1 Inverting Bell matrices . 13.3.2 The Leibniz formula + 171 172 13.3.3 The inverse series . 173 13.4 Developments ...
... matrix representation . 165 13.2.1 An important inversion formula . 169 13.3 The Lagrange inversion formula . 171 13.3.1 Inverting Bell matrices . 13.3.2 The Leibniz formula + 171 172 13.3.3 The inverse series . 173 13.4 Developments ...
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