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 xiv
... Fredholm formalism Appendix A Formulary A.1 General formulas A.2 Algebra A.3 Stochastic matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 283 283 287 288 A.4 Circulant matrices 289 A.5 Bell polynomials 293 A.5.1 Orthogonal ...
... Fredholm formalism Appendix A Formulary A.1 General formulas A.2 Algebra A.3 Stochastic matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 283 283 287 288 A.4 Circulant matrices 289 A.5 Bell polynomials 293 A.5.1 Orthogonal ...
Página xv
... 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 gases . 306 Bibliography 309 Index 315 PART ...
... 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 gases . 306 Bibliography 309 Index 315 PART ...
Página 4
... of activity on the subject . Here is given that predominant in Matrix Theory . We shall find another in Fredholm Theory ( Section 16.6 ) . - is the minimal polynomial of M. The minimal polynomial 4 Some fundamental notions.
... of activity on the subject . Here is given that predominant in Matrix Theory . We shall find another in Fredholm Theory ( Section 16.6 ) . - is the minimal polynomial of M. The minimal polynomial 4 Some fundamental notions.
Página 150
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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