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. |
Dentro del libro
Resultados 6-10 de 41
Página 8
... projectors . Such eigenpro- jectors provide , under a simple condition , an immediate adaptation to matrices of any function defined by a Taylor series . Suppose a function F ( X ) is given which can be expanded as a power series ∞ F ...
... projectors . Such eigenpro- jectors provide , under a simple condition , an immediate adaptation to matrices of any function defined by a Taylor series . Suppose a function F ( X ) is given which can be expanded as a power series ∞ F ...
Página 10
... projectors , that is , idempotents , objects satisfying Zk ; this equation , in the form . Z2 = En Z ( k ) ] rn [ Z ( k ) ] ns = [ Z ( k ) ] rs › shows that Z ( k ) has for columns its own eigenvectors with eigen- value 1 ; indeed ...
... projectors , that is , idempotents , objects satisfying Zk ; this equation , in the form . Z2 = En Z ( k ) ] rn [ Z ( k ) ] ns = [ Z ( k ) ] rs › shows that Z ( k ) has for columns its own eigenvectors with eigen- value 1 ; indeed ...
Página 11
... projectors frequently used in Quantum Mechanics . Their simplicity comes from the supposed normal character of M. We shall say a little more on normal matrices in section 1.4 . A set of N powers of M is enough to fix the projector basis ...
... projectors frequently used in Quantum Mechanics . Their simplicity comes from the supposed normal character of M. We shall say a little more on normal matrices in section 1.4 . A set of N powers of M is enough to fix the projector basis ...
Página 12
... projector basis . Actually , any set of independent polynomials in M could be used as the starting basis . In particular , once we know them , the projectors themselves can be taken as the basis polynomials and the above determinant ...
... projector basis . Actually , any set of independent polynomials in M could be used as the starting basis . In particular , once we know them , the projectors themselves can be taken as the basis polynomials and the above determinant ...
Página 13
... projectors themselves will be presented in Section 15.1 . Comment 1.3.2 That functions of matrices are completely determined by their spec- tra is justified on much more general grounds . Matrix algebras are very particular kinds of von ...
... projectors themselves will be presented in Section 15.1 . Comment 1.3.2 That functions of matrices are completely determined by their spec- tra is justified on much more general grounds . Matrix algebras are very particular kinds of von ...
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