Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell MatricesWorld Scientific, 2001 - 323 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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Stochastic, Circulant, and Bell Matrices Ruben Aldrovandi. Preface Contents BASICS Chapter 1 Some fundamental notions 1.1 Definitions 1.2 Components of a matrix 1.3 Matrix functions 1.3.1 Nondegenerate matrices 1.3.2 Degenerate matrices ...
Stochastic, Circulant, and Bell Matrices Ruben Aldrovandi. Preface Contents BASICS Chapter 1 Some fundamental notions 1.1 Definitions 1.2 Components of a matrix 1.3 Matrix functions 1.3.1 Nondegenerate matrices 1.3.2 Degenerate matrices ...
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... CIRCULANT MATRICES Chapter 8 Prelude 81 Chapter 9 Definition and main properties 83 9.1 Bases • 93 9.2 Double Fourier transform 95 9.3 Random walks 96 Chapter 10 Discrete quantum mechanics 10.1 Introduction . 99 99 10.2 Weyl ...
... CIRCULANT MATRICES Chapter 8 Prelude 81 Chapter 9 Definition and main properties 83 9.1 Bases • 93 9.2 Double Fourier transform 95 9.3 Random walks 96 Chapter 10 Discrete quantum mechanics 10.1 Introduction . 99 99 10.2 Weyl ...
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... matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 283 283 287 288 A.4 Circulant matrices 289 A.5 Bell polynomials 293 A.5.1 Orthogonal polynomials 297 A.5.2 Differintegration , derivatives of Bell polynomials 298 A.6 ...
... matrices 247 248 251 253 255 260 • 263 264 267 268 270 274 283 283 287 288 A.4 Circulant matrices 289 A.5 Bell polynomials 293 A.5.1 Orthogonal polynomials 297 A.5.2 Differintegration , derivatives of Bell polynomials 298 A.6 ...
Contenido
STOCHASTIC MATRICES | 19 |
CIRCULANT MATRICES | 79 |
BELL MATRICES | 147 |
Appendix A Formulary | 283 |
Bibliography | 309 |
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