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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Resultados 1-5 de 58
Página viii
... formulas usually presented with ellipses in the end , a true nightmare for algebraic computation . Those expressions in- clude relationships between determinants and traces , coefficients and roots of polynomials , virial coefficients ...
... formulas usually presented with ellipses in the end , a true nightmare for algebraic computation . Those expressions in- clude relationships between determinants and traces , coefficients and roots of polynomials , virial coefficients ...
Página ix
... formulas used in finding and / or checking them . The only way we break with standard editing is by the presence of Comments , which con- tain information additional to the main text and may be omitted in a first reading . Matrices ...
... formulas used in finding and / or checking them . The only way we break with standard editing is by the presence of Comments , which con- tain information additional to the main text and may be omitted in a first reading . Matrices ...
Página xiii
... 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 . 13.4.1 A useful pseudo - recursion 13.4.2 Relations to ...
... 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 . 13.4.1 A useful pseudo - recursion 13.4.2 Relations to ...
Página xiv
... formula . 16.3.1.1 Relativistic gases , continued 16.3.2 Only connected graphs matter 16.4 Braid statistics 16.5 ... formulas A.2 Algebra A.3 Stochastic matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 283 283 287 288 A.4 ...
... formula . 16.3.1.1 Relativistic gases , continued 16.3.2 Only connected graphs matter 16.4 Braid statistics 16.5 ... formulas A.2 Algebra A.3 Stochastic matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 283 283 287 288 A.4 ...
Página 7
... formula a meaningful , convergent expression . Notice on the other hand that , besides the Cayley - Hamilton theorem , which is valid for every matrix , the only assumption made has been that the eigenvalues are distinct . No use has ...
... formula a meaningful , convergent expression . Notice on the other hand that , besides the Cayley - Hamilton theorem , which is valid for every matrix , the only assumption made has been that the eigenvalues are distinct . No use has ...
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