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 41
Página xii
... Projectors and asymptotics 6.4 6.3.1 The 1 - dimensional Ising model Continuum time 6.4.1 · 6.4.2 Passage to the continuum Hamiltonian language 35 40 41 45 45 50 53 • 58 60 60 61 63 63 · 67 72 74 77 78 Chapter 7 Equilibrium ...
... Projectors and asymptotics 6.4 6.3.1 The 1 - dimensional Ising model Continuum time 6.4.1 · 6.4.2 Passage to the continuum Hamiltonian language 35 40 41 45 45 50 53 • 58 60 60 61 63 63 · 67 72 74 77 78 Chapter 7 Equilibrium ...
Página xiii
... 14.2 Symmetric functions 14.3 Polynomials 14.4 Characteristic polynomials . 176 176 178 · 180 181 Determinants and traces 183 183 186 193 196 14.5 Lie algebras invariants 14.5.1 Characteristic classes Chapter 15 Projectors Contents xiii.
... 14.2 Symmetric functions 14.3 Polynomials 14.4 Characteristic polynomials . 176 176 178 · 180 181 Determinants and traces 183 183 186 193 196 14.5 Lie algebras invariants 14.5.1 Characteristic classes Chapter 15 Projectors Contents xiii.
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 6
... projector . When the eigen- values are distinct , we can divide Z1 by ( A1 – A2 ) ( A1 – À3 ) and define a new projector ( M – \ 2I ) ( M – λ3I ) -- Z1 ( A1 – A2 ) ( A1 – λ3 ) ( 1.7 ) This is a true eigenprojector . It is an idempotent ...
... projector . When the eigen- values are distinct , we can divide Z1 by ( A1 – A2 ) ( A1 – À3 ) and define a new projector ( M – \ 2I ) ( M – λ3I ) -- Z1 ( A1 – A2 ) ( A1 – λ3 ) ( 1.7 ) This is a true eigenprojector . It is an idempotent ...
Página 7
... projectors Z2 and Z3 . The product of any two distinct Z's is proportional to Am ( M ) and , consequently , vanishes . In short , Zk Zk ' = Skk ' Zk and tr ( Zk Zk ' ) = dkk ' · Direct computation shows that I = Σk Zk , which multiplied ...
... projectors Z2 and Z3 . The product of any two distinct Z's is proportional to Am ( M ) and , consequently , vanishes . In short , Zk Zk ' = Skk ' Zk and tr ( Zk Zk ' ) = dkk ' · Direct computation shows that I = Σk Zk , which multiplied ...
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