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
... A.5.2 Differintegration , derivatives of Bell polynomials 298 A.6 Determinants , minors and traces 298 A.6.1 Symmetric functions 299 A.6.2 Polynomials . A.6.3 Characteristic polynomials and classes 300 301 xiv Contents.
... A.5.2 Differintegration , derivatives of Bell polynomials 298 A.6 Determinants , minors and traces 298 A.6.1 Symmetric functions 299 A.6.2 Polynomials . A.6.3 Characteristic polynomials and classes 300 301 xiv Contents.
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... derivatives at each eigenvalue : F ( x ) = Σ - j = 1 AM ( 1 ) ( A — Aj ) A'm ( Aj ) F ( X ) . ( 1.21 ) Expression ( 1.19 ) can be put into an elegant form , stating the vanishing of a formal determinant : F ( M ) F ( 1 ) F ( \ 2 ) F ...
... derivatives at each eigenvalue : F ( x ) = Σ - j = 1 AM ( 1 ) ( A — Aj ) A'm ( Aj ) F ( X ) . ( 1.21 ) Expression ( 1.19 ) can be put into an elegant form , stating the vanishing of a formal determinant : F ( M ) F ( 1 ) F ( \ 2 ) F ...
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... derivatives with respect to λ3 and after that put 3 1 . All this generalizes to higher degeneracies ( with corresponding higher derivatives ) and to higher - order matrices . Suppose that there are m distinct eigenvalues , and denote by ...
... derivatives with respect to λ3 and after that put 3 1 . All this generalizes to higher degeneracies ( with corresponding higher derivatives ) and to higher - order matrices . Suppose that there are m distinct eigenvalues , and denote by ...
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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