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Special matrices of mathematical physics : stochastic, circulant, and Bell matrices

Author: R Aldrovandi
Publisher: Singapore ; River Edge, N.J. : World Scientific, ©2001.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This work expounds three special kinds of matrices that are of physical interest, centring on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, non-equilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Aldrovandi, R. (Ruben).
Special matrices of mathematical physics.
Singapore ; River Edge, N.J. : World Scientific, ©2001
(DLC) 2001026864
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: R Aldrovandi
ISBN: 9789812799838 9812799834 1281951390 9781281951397
OCLC Number: 505150634
Description: 1 online resource (xv, 323 pages)
Contents: Ch. 1. Some fundamental notions. 1.1. Definitions. 1.2. Components of a matrix. 1.3. Matrix functions. 1.4. Normal matrices --
ch. 2. Evolving systems --
ch. 3. Markov chains. 3.1. Non-negative matrices. 3.2. General properties --
ch. 4. Glass transition --
ch. 5. The Kerner model. 5.1. A simple example: Se-As glass --
ch. 6. Formal developments. 6.1. Spectral aspects. 6.2. Reducibility and regularity. 6.3. Projectors and asymptotics. 6.4. Continuum time --
ch. 7. Equilibrium, dissipation and ergodicity. 7.1. Recurrence, transience and periodicity. 7.2. Detailed balancing and reversibility. 7.3. Ergodicity --
ch. 8. Prelude --
ch. 9. Definition and main properties. 9.1. Bases. 9.2. Double Fourier transform. 9.3. Random walks --
ch. 10. Discrete quantum mechanics. 10.1. Introduction. 10.2. Weyl-Heisenberg groups. 10.3. Weyl-Wigner transformations. 10.4. Braiding and quantum groups --
ch. 11. Quantum symplectic structure. 11.1. Matrix differential geometry. 11.2. The symplectic form. 11.3. The quantum fabric --
ch. 12. An organizing tool --
ch. 13. Bell polynomials. 13.1. Definition and elementary properties. 13.2. The matrix representation. 13.3. The Lagrange inversion formula. 13.4. Developments --
ch. 14. Determinants and traces. 14.1. Introduction. 14.2. Symmetric functions. 14.3. Polynomials. 14.4. Characteristic polynomials. 14.5. Lie algebras invariants --
ch. 15. Projectors and iterates. 15.1. Projectors, revisited. 15.2. Continuous iterates --
ch. 16. Gases: real and ideal. 16.1. Microcanonical ensemble. 16.2. The canonical ensemble. 16.3. The grand canonical ensemble. 16.4. Braid statistics. 16.5. Condensation theories. 16.6. The Fredholm formalism.
Responsibility: R. Aldrovandi.

Abstract:

This work expounds three special kinds of matrices that are of physical interest, centring on physical examples: stochastic matrices, circulant matrices, and bell matrices.  Read more...

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<http:\/\/www.worldcat.org\/oclc\/505150634<\/a>> # Special matrices of mathematical physics : stochastic, circulant, and Bell matrices<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:CreativeWork<\/a>, schema:MediaObject<\/a>, schema:Book<\/a> ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"505150634<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/si<\/a>> ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/802616892#Place\/singapore<\/a>> ; # Singapore<\/span>\n\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/802616892#Place\/river_edge_n_j<\/a>> ; # River Edge, N.J.<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/id.worldcat.org\/fast\/1012399<\/a>> ; # Matrices<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/id.worldcat.org\/fast\/1012104<\/a>> ; # Mathematical physics<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/530.1529434\/e21\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/802616892#Topic\/science_physics_mathematical_&_computational<\/a>> ; # SCIENCE--Physics--Mathematical & Computational<\/span>\n\u00A0\u00A0\u00A0\nschema:bookFormat<\/a> schema:EBook<\/a> ;\u00A0\u00A0\u00A0\nschema:copyrightYear<\/a> \"2001<\/span>\" ;\u00A0\u00A0\u00A0\nschema:creator<\/a> <http:\/\/viaf.org\/viaf\/64113454<\/a>> ; # Ruben Aldrovandi<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2001<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"This work expounds three special kinds of matrices that are of physical interest, centring on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, non-equilibrium, 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 non-commutative 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.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Ch. 1. Some fundamental notions. 1.1. Definitions. 1.2. Components of a matrix. 1.3. Matrix functions. 1.4. Normal matrices -- ch. 2. Evolving systems -- ch. 3. Markov chains. 3.1. Non-negative matrices. 3.2. General properties -- ch. 4. Glass transition -- ch. 5. The Kerner model. 5.1. A simple example: Se-As glass -- ch. 6. Formal developments. 6.1. Spectral aspects. 6.2. Reducibility and regularity. 6.3. Projectors and asymptotics. 6.4. Continuum time -- ch. 7. Equilibrium, dissipation and ergodicity. 7.1. Recurrence, transience and periodicity. 7.2. Detailed balancing and reversibility. 7.3. Ergodicity -- ch. 8. Prelude -- ch. 9. Definition and main properties. 9.1. Bases. 9.2. Double Fourier transform. 9.3. Random walks -- ch. 10. Discrete quantum mechanics. 10.1. Introduction. 10.2. Weyl-Heisenberg groups. 10.3. Weyl-Wigner transformations. 10.4. Braiding and quantum groups -- ch. 11. Quantum symplectic structure. 11.1. Matrix differential geometry. 11.2. The symplectic form. 11.3. The quantum fabric -- ch. 12. An organizing tool -- ch. 13. Bell polynomials. 13.1. Definition and elementary properties. 13.2. The matrix representation. 13.3. The Lagrange inversion formula. 13.4. Developments -- ch. 14. Determinants and traces. 14.1. Introduction. 14.2. Symmetric functions. 14.3. Polynomials. 14.4. Characteristic polynomials. 14.5. Lie algebras invariants -- ch. 15. Projectors and iterates. 15.1. Projectors, revisited. 15.2. Continuous iterates -- ch. 16. Gases: real and ideal. 16.1. Microcanonical ensemble. 16.2. The canonical ensemble. 16.3. The grand canonical ensemble. 16.4. Braid statistics. 16.5. Condensation theories. 16.6. 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