Special Matrices Of Mathematical Physics: Stochastic, Circulant And Bell MatricesThis 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
Those expressions include relationships between determinants and traces, coefficients and roots of polynomials, virial coefficients and configuration integrals, besides Lie algebra invariants of various types, from Casimir operators to ...
Those expressions include relationships between determinants and traces, coefficients and roots of polynomials, virial coefficients and configuration integrals, besides Lie algebra invariants of various types, from Casimir operators to ...
Página xii
103 10.2.1 Weyl's operators . . . . . . . . . . . . . . . . . . . . . . 104 10.2.2 The Schwinger basis . . . . . . . . . . . . . . . . . . . . 105 10.2.3 Continuum limit and interpretation . . . . . . . . . . . 110 10.3 Weyl-Wigner ...
103 10.2.1 Weyl's operators . . . . . . . . . . . . . . . . . . . . . . 104 10.2.2 The Schwinger basis . . . . . . . . . . . . . . . . . . . . 105 10.2.3 Continuum limit and interpretation . . . . . . . . . . . 110 10.3 Weyl-Wigner ...
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Degenerate matrices As a rule, physicists dislike degenerate matrices and/or operators. In Quantum Mechanics, for example, they proceed to increase the number of operators up to the point at which all degeneracy is removed.
Degenerate matrices As a rule, physicists dislike degenerate matrices and/or operators. In Quantum Mechanics, for example, they proceed to increase the number of operators up to the point at which all degeneracy is removed.
Página 18
The importance of normal operators in quantum physics is not strange to this fact. The decomposition into components, however, holds also when M is not normal (as a Bell matrix), though in that case, as said, the components may lose ...
The importance of normal operators in quantum physics is not strange to this fact. The decomposition into components, however, holds also when M is not normal (as a Bell matrix), though in that case, as said, the components may lose ...
Página 27
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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 Cayley–Hamilton theorem 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 eigenvalues eigenvectors entries equation equilibrium evolution example fermions formalism formula Fourier transformations Fredholm geometry given glass grand canonical partition Hamiltonian Hopf algebras identity imprimitive invariant inverse irreducible iterate Ksas Ksasa leads Lie algebra Markov chain noncommutative notation obtained operator particles permutation phase space Poisson bracket powers projectors properties Quantum Mechanics recursion representation stochastic matrix summation symmetric functions symmetric group symplectic Taylor coefficients theorem totally regular unitary values variables vector virial Wigner functions
Información bibliográfica
| Título | Special Matrices Of Mathematical Physics: Stochastic, Circulant And Bell Matrices |
| Autor | Ruben Aldrovandi |
| Editor | World Scientific, 2001 |
| ISBN | 9814490466, 9789814490467 |
| Largo | 340 páginas |
| Exportar cita | BiBTeX EndNote RefMan |