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 10
... eigenvalues of M are distinct . We shall first describe that case , and later adapt the results to the degenerate ... eigenvalue Aki ( 9 ) if M is a normal matrix and U - 1MU = Mdiagonal , then the entries of Z are given by ( Zk ) rs ...
... eigenvalues of M are distinct . We shall first describe that case , and later adapt the results to the degenerate ... eigenvalue Aki ( 9 ) if M is a normal matrix and U - 1MU = Mdiagonal , then the entries of Z are given by ( Zk ) rs ...
Página 12
... eigenvalue : F ( x ) = Σ - j = 1 AM ( 1 ) ( A — Aj ) A'm ( Aj ) F ( X ) . ( 1.21 ) Expression ( 1.19 ) can be put into ... eigenvalues of M and the detailed form of its first ( N - 1 ) powers . What we have done is to start from a basis ...
... eigenvalue : F ( x ) = Σ - j = 1 AM ( 1 ) ( A — Aj ) A'm ( Aj ) F ( X ) . ( 1.21 ) Expression ( 1.19 ) can be put into ... eigenvalues of M and the detailed form of its first ( N - 1 ) powers . What we have done is to start from a basis ...
Página 13
... 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 completely determined by their ...
... 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 completely determined by their ...
Página 15
... eigenvalues , and denote by m ; the multiplicity of the j - th eigenvalue À¡ . For each such eigenvalue A , there will be components Zj1 , Zj2 , · · · Zjm ; · The general form of F ( M ) will be m F ( mj − 1 ) ( \ j Matrix functions 111 ...
... eigenvalues , and denote by m ; the multiplicity of the j - th eigenvalue À¡ . For each such eigenvalue A , there will be components Zj1 , Zj2 , · · · Zjm ; · The general form of F ( M ) will be m F ( mj − 1 ) ( \ j Matrix functions 111 ...
Página 17
... eigenvalues are real , the matrices represent quantum mechanical ob- servables . An N x N matrix M , we repeat , is ... eigenvalue of the corresponding projector : Zk V ( k ' ) = dkk ' V ( k ) . One of the most important properties of ...
... eigenvalues are real , the matrices represent quantum mechanical ob- servables . An N x N matrix M , we repeat , is ... eigenvalue of the corresponding projector : Zk V ( k ' ) = dkk ' V ( k ) . One of the most important properties of ...
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