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 46
Página viii
... theory of gases , promise to be instrumental in the study of chaotic mappings . Stochastic matrices govern , through repeated iteration , the time evo- lution of probability distributions of which they are independent . The example ...
... theory of gases , promise to be instrumental in the study of chaotic mappings . Stochastic matrices govern , through repeated iteration , the time evo- lution of probability distributions of which they are independent . The example ...
Página ix
... theory . The text is divided into four Parts : one for the general background and one for each kind of matrix . Up to references to the background introduc- tion , the Parts are tentatively self - contained , which accounts for a ...
... theory . The text is divided into four Parts : one for the general background and one for each kind of matrix . Up to references to the background introduc- tion , the Parts are tentatively self - contained , which accounts for a ...
Página xiv
... theories 16.5.1 Mayer's model for condensation . 16.5.2 The Lee - Yang theory 16.6 The Fredholm formalism Appendix A Formulary A.1 General formulas A.2 Algebra A.3 Stochastic matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 ...
... theories 16.5.1 Mayer's model for condensation . 16.5.2 The Lee - Yang theory 16.6 The Fredholm formalism Appendix A Formulary A.1 General formulas A.2 Algebra A.3 Stochastic matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 ...
Página xv
... 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 gases . 306 Bibliography 309 Index 315 PART 1 BASICS ...
... 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 gases . 306 Bibliography 309 Index 315 PART 1 BASICS ...
Página 3
... Theory in general is covered in Gantmacher's classic [ 1 ] . 1.1 Definitions ( 1 ) Given an N × N matrix M , its characteristic ́matrix is XI – M , a function of M , of the N × N identity matrix I and of the complex variable A. ( 2 ) ...
... Theory in general is covered in Gantmacher's classic [ 1 ] . 1.1 Definitions ( 1 ) Given an N × N matrix M , its characteristic ́matrix is XI – M , a function of M , of the N × N identity matrix I and of the complex variable A. ( 2 ) ...
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