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 4
... eigenvalues are all distinct , M is said to be nondegenerate . M is degenerate if at least one root is multiple ... eigenvalue contributes to the product above with as many factors as its multiplicity . N Σo cjXj ( 8 ) Writing the ...
... eigenvalues are all distinct , M is said to be nondegenerate . M is degenerate if at least one root is multiple ... eigenvalue contributes to the product above with as many factors as its multiplicity . N Σo cjXj ( 8 ) Writing the ...
Página 5
... eigenvalues and , as particular cases , so do symmetric matrices . More about normal matrices is said below , in Section 1.4 . ( 12 ) An account of non - negative matrices is given in Section 3.1 . ( 13 ) An algebra is a vector space V ...
... eigenvalues and , as particular cases , so do symmetric matrices . More about normal matrices is said below , in Section 1.4 . ( 12 ) An account of non - negative matrices is given in Section 3.1 . ( 13 ) An algebra is a vector space V ...
Página 6
... eigenvalue were multiple , but we shall suppose that this is not the case . Let us isolate one of the factors , say that including the eigenvalue A1 , corresponding to some eigenvector V1 , and look at the properties of the remaining ...
... eigenvalue were multiple , but we shall suppose that this is not the case . Let us isolate one of the factors , say that including the eigenvalue A1 , corresponding to some eigenvector V1 , and look at the properties of the remaining ...
Página 7
... eigenvalues λ2 and λ3 , then Z1V2 Z1V3 = 0 . = 0 , The above considerations can be repeated for each factor in ( 1.5 ) , lead- ing to eigenmatrices Z2 , Z3 and , as long as the eigenvalues are different , to the corresponding projectors ...
... eigenvalues λ2 and λ3 , then Z1V2 Z1V3 = 0 . = 0 , The above considerations can be repeated for each factor in ( 1.5 ) , lead- ing to eigenmatrices Z2 , Z3 and , as long as the eigenvalues are different , to the corresponding projectors ...
Página 8
... eigenvalue . For nondegenerate ma- trices , these components are orthonormal projectors . Such eigenpro- jectors ... eigenvalues A1 , A2 , ··· , AN , there exists a set of matrices { Z ; [ M ] } constituting a matrix basis in terms ...
... eigenvalue . For nondegenerate ma- trices , these components are orthonormal projectors . Such eigenpro- jectors ... eigenvalues A1 , A2 , ··· , AN , there exists a set of matrices { Z ; [ M ] } constituting a matrix basis in terms ...
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