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. |
Dentro del libro
Página xiv
287 A.3 Stochastic matrices . . . . . . . . . . . . . . . . . . . . . . . . . 288 A.4 Circulant matrices . . . . . . . . . . . . . . . . . . . . . . . . . 289 A.5 Bell polynomials .
287 A.3 Stochastic matrices . . . . . . . . . . . . . . . . . . . . . . . . . 288 A.4 Circulant matrices . . . . . . . . . . . . . . . . . . . . . . . . . 289 A.5 Bell polynomials .
Página 3
Chapter 1 Some fundamental notions We here recall some basic concepts on matrices, with the main purpose of fixing notation and terminology. Only ideas and results necessary to the discussion of the particular kinds of matrices we shall ...
Chapter 1 Some fundamental notions We here recall some basic concepts on matrices, with the main purpose of fixing notation and terminology. Only ideas and results necessary to the discussion of the particular kinds of matrices we shall ...
Página 4
There roots \k, already introduced in the last equality of (1.1), are the eigenvalues of M. For each k, there exists an eigenvector vk, a nonvanishing N × 1 matrix (that is, a column) satisfying Mvs = \k vs. If the eigenvalues are all ...
There roots \k, already introduced in the last equality of (1.1), are the eigenvalues of M. For each k, there exists an eigenvector vk, a nonvanishing N × 1 matrix (that is, a column) satisfying Mvs = \k vs. If the eigenvalues are all ...
Página 5
Given a complex N × N matrix M, its adjoint (or Hermitian conjugate) Mf is the matrix whose entries are Miss = M*ji. For real matrices, the adjoint coincides with the transpose: M = M*. To ease typewriting, we shall frequently indicate ...
Given a complex N × N matrix M, its adjoint (or Hermitian conjugate) Mf is the matrix whose entries are Miss = M*ji. For real matrices, the adjoint coincides with the transpose: M = M*. To ease typewriting, we shall frequently indicate ...
Página 6
1.2 Components of a matrix Every matrix M with spectrum X = {X1, X2, X3, ... , XN } can be decomposed in terms of certain “components” Zk, which are eigenmatrices (MZk = Xk Zk). This spectral decomposition M = XCs X,Zo is intimately ...
1.2 Components of a matrix Every matrix M with spectrum X = {X1, X2, X3, ... , XN } can be decomposed in terms of certain “components” Zk, which are eigenmatrices (MZk = Xk Zk). This spectral decomposition M = XCs X,Zo is intimately ...
Comentarios de la gente - Escribir un comentario
No encontramos ningún comentario en los lugares habituales.
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 |