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 xiii
... 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.
... 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.
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... functions 16.2.1.1 Relativistic gases , starting 16.2.1.2 Quantum correlations 16.3 The grand canonical ensemble ... Symmetric functions 299 A.6.2 Polynomials . A.6.3 Characteristic polynomials and classes 300 301 xiv Contents.
... functions 16.2.1.1 Relativistic gases , starting 16.2.1.2 Quantum correlations 16.3 The grand canonical ensemble ... Symmetric functions 299 A.6.2 Polynomials . A.6.3 Characteristic polynomials and classes 300 301 xiv Contents.
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... symmetric matrices . More about normal matrices is said below , in Section ... antisymmetric , a b = - b * a , and the Jacobi identity ( a * b ) * c + ( c ... functions ( Section 14.2 ) . In principle , the alphabet can be infinite and ...
... symmetric matrices . More about normal matrices is said below , in Section ... antisymmetric , a b = - b * a , and the Jacobi identity ( a * b ) * c + ( c ... functions ( Section 14.2 ) . In principle , the alphabet can be infinite and ...
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... symmetric functions of the eigenvalues of M , which will be examined in Section 14.2 [ see Eq . ( 14.46 ) , for example ] . The projectors themselves will be presented in Section 15.1 . Comment 1.3.2 That functions of matrices are ...
... symmetric functions of the eigenvalues of M , which will be examined in Section 14.2 [ see Eq . ( 14.46 ) , for example ] . The projectors themselves will be presented in Section 15.1 . Comment 1.3.2 That functions of matrices are ...
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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