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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... Cayley - Hamilton theorem [ 2 ] states that , for any matrix M , the characteristic polynomial is an annihilating polynomial : ---- — AM ( M ) = ( M - λ1 ) ( M – λ2 ) ( M – λ3 ) ... ( M – An − 1 ) ( M – λn ) = 0 . ( 1.3 ) In simple ...
... Cayley - Hamilton theorem [ 2 ] states that , for any matrix M , the characteristic polynomial is an annihilating polynomial : ---- — AM ( M ) = ( M - λ1 ) ( M – λ2 ) ( M – λ3 ) ... ( M – An − 1 ) ( M – λn ) = 0 . ( 1.3 ) In simple ...
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... Cayley - Hamilton theorem takes , in the present case , the form AM ( M ) = ( M- \ 1I ) ( M — \ 1⁄2I ) ( M – λ3I ) = 0 . ( 1.5 ) There would be repeated factors if some eigenvalue were multiple , but we shall suppose that this is not ...
... Cayley - Hamilton theorem takes , in the present case , the form AM ( M ) = ( M- \ 1I ) ( M — \ 1⁄2I ) ( M – λ3I ) = 0 . ( 1.5 ) There would be repeated factors if some eigenvalue were multiple , but we shall suppose that this is not ...
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... Cayley - Hamilton theorem , which is valid for every matrix , the only assumption made has been that the eigenvalues are distinct . No use has been made of any further special property . What has been done above holds consequently for ...
... Cayley - Hamilton theorem , which is valid for every matrix , the only assumption made has been that the eigenvalues are distinct . No use has been made of any further special property . What has been done above holds consequently for ...
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... Cayley - Hamilton theorem : the equation △ B ( M ) = 0 provides MN in terms of lower powers of M , so that all the higher powers of M can be computed from those between M ° and MN - 1 . Inversion of the above expressions for the powers ...
... Cayley - Hamilton theorem : the equation △ B ( M ) = 0 provides MN in terms of lower powers of M , so that all the higher powers of M can be computed from those between M ° and MN - 1 . Inversion of the above expressions for the powers ...
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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