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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Resultados 6-10 de 65
Página 6
... properties of the remaining expression , To begin with , 21 Z1 = ( M - 2I ) ( M — λ3I ) . - Ž1V1 = ( A1 − A2 ) ( A1 – A3 ) V1 . ( 1.6 ) As any other contribution to the trace vanishes , the trace of Ż1 is also ( A1 — A2 ) ( A1 – A3 ) ...
... properties of the remaining expression , To begin with , 21 Z1 = ( M - 2I ) ( M — λ3I ) . - Ž1V1 = ( A1 − A2 ) ( A1 – A3 ) V1 . ( 1.6 ) As any other contribution to the trace vanishes , the trace of Ż1 is also ( A1 — A2 ) ( A1 – A3 ) ...
Página 7
... properties above it follows that Mmm Zk ( 1.8 ) = Σm Cmzm , a ma- Στη CmMm = Consequently , given any power series function F ( z ) trix function F ( M ) can be formally defined by F ( M ) Σk Σm Cmλm Zk , or F ( M ) = ΣkF ( \ k ) Zk ...
... properties above it follows that Mmm Zk ( 1.8 ) = Σm Cmzm , a ma- Στη CmMm = Consequently , given any power series function F ( z ) trix function F ( M ) can be formally defined by F ( M ) Σk Σm Cmλm Zk , or F ( M ) = ΣkF ( \ k ) Zk ...
Página 10
... properties of the eigenmatrices Zx [ M ] of a nondegenerate matrix M : ( 1 ) the Z's are linearly independent and nonvanishing ; ( 2 ) the basis { Z [ M ] } depends on M , but is the same for every function F ( M ) ; thus , any F ( M ) ...
... properties of the eigenmatrices Zx [ M ] of a nondegenerate matrix M : ( 1 ) the Z's are linearly independent and nonvanishing ; ( 2 ) the basis { Z [ M ] } depends on M , but is the same for every function F ( M ) ; thus , any F ( M ) ...
Página 16
... properties listed on p . 10 : they are linearly independent , nonvanishing and commute with each other and with M. The remaining properties are , however , absent in the generic degenerate case . In particular , the trace properties and ...
... properties listed on p . 10 : they are linearly independent , nonvanishing and commute with each other and with M. The remaining properties are , however , absent in the generic degenerate case . In particular , the trace properties and ...
Página 17
... V ( k ) . One of the most important properties of normal ma- trices comes out at this point : the eigenvectors V ( k ) are necessarily linearly independent and , in consequence , constitute a base in Normal matrices 17 1.4 Normal matrices.
... V ( k ) . One of the most important properties of normal ma- trices comes out at this point : the eigenvectors V ( k ) are necessarily linearly independent and , in consequence , constitute a base in Normal matrices 17 1.4 Normal matrices.
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