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
... algebraic computation . Those expressions in- clude relationships between determinants and traces , coefficients and roots of polynomials , virial coefficients and configuration integrals , besides Lie algebra invariants of various ...
... algebraic computation . Those expressions in- clude relationships between determinants and traces , coefficients and roots of polynomials , virial coefficients and configuration integrals , besides Lie algebra invariants of various ...
Página xiv
Ruben Aldrovandi. 14.5 Lie algebras invariants 14.5.1 Characteristic classes Chapter 15 Projectors and iterates 15.1 Projectors , revisited 15.2 Continuous iterates 200 203 207 207 211 15.2.1 An application to turbulence 15.2.2 The ...
Ruben Aldrovandi. 14.5 Lie algebras invariants 14.5.1 Characteristic classes Chapter 15 Projectors and iterates 15.1 Projectors , revisited 15.2 Continuous iterates 200 203 207 207 211 15.2.1 An application to turbulence 15.2.2 The ...
Página 5
... algebra with their usual product , and a Lie algebra with the commutator . ( 14 ) The following terminology will be frequently used . We call an al- phabet any ordered set of quantities x1 , x2 , x3 , ... , ÎN and indicate it by the ...
... algebra with their usual product , and a Lie algebra with the commutator . ( 14 ) The following terminology will be frequently used . We call an al- phabet any ordered set of quantities x1 , x2 , x3 , ... , ÎN and indicate it by the ...
Página 13
... algebras are very particular kinds of von Neumann algebras and it is a very strong result of the still more general ... Lie algebra will be W a1J1 + a2J2 + α3J3 0 -03 α3 -α2 απ -α1 } αι = where the variables a are angular parameters ...
... algebras are very particular kinds of von Neumann algebras and it is a very strong result of the still more general ... Lie algebra will be W a1J1 + a2J2 + α3J3 0 -03 α3 -α2 απ -α1 } αι = where the variables a are angular parameters ...
Página 17
... Lie algebra generic matrix is degenerate turns up in the Galilei group [ 4 ] . 1.4 Normal matrices As they are specially simple and of fundamental importance to Quantum Mechanics , normal matrices deserve particular attention . They are ...
... Lie algebra generic matrix is degenerate turns up in the Galilei group [ 4 ] . 1.4 Normal matrices As they are specially simple and of fundamental importance to Quantum Mechanics , normal matrices deserve particular attention . They are ...
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