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 3
1.1 Definitions (1) Given an N × N matrix M, its characteristic matria is XI – M, a function of M, of the N × N identity matrix I and of the complex variable X. (2) The characteristic polynomial of M is the determinant of the ...
1.1 Definitions (1) Given an N × N matrix M, its characteristic matria is XI – M, a function of M, of the N × N identity matrix I and of the complex variable X. (2) The characteristic polynomial of M is the determinant of the ...
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Here is given that predominant in Matrix Theory. We shall find another in Fredholm Theory (Section 16.6). (10) (11) (12) (13) (14) is the minimal polynomial of 4 Some fundamental notions.
Here is given that predominant in Matrix Theory. We shall find another in Fredholm Theory (Section 16.6). (10) (11) (12) (13) (14) is the minimal polynomial of 4 Some fundamental notions.
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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 ...
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From the properties above it follows that M” = XXX: Zs. (1.8) Consequently, given any power series function F(z) = XD., cm2”, a matrix function F(M) can be formally defined by F(M) = XD., ...
From the properties above it follows that M” = XXX: Zs. (1.8) Consequently, given any power series function F(z) = XD., cm2”, a matrix function F(M) can be formally defined by F(M) = XD., ...
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Suppose a function F(X) is given which can be expanded as a power series Co F(A) =XD ce(X = X0)* k=0 inside a convergence circle |X – Xol 3 r. Then the function F(M), whose argument is some given N × N matrix M, is defined by CO F(M) ...
Suppose a function F(X) is given which can be expanded as a power series Co F(A) =XD ce(X = X0)* k=0 inside a convergence circle |X – Xol 3 r. Then the function F(M), whose argument is some given N × N matrix M, is defined by CO F(M) ...
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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 |