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Mathematics in Science and Engineering, From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems

Mathematics in Science and Engineering, From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems - Cheng, Daizhan - ISBN: 9780128178010
Prijs: € 142,80 (onder voorbehoud)
Beschikbaarheid: Levertijd tussen de 5 en 15 werkdagen. Geen retour recht.
Bindwijze: Boek, Paperback (21-05-2019)
Genre: Toepassingsgerichte wiskunde
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Beschrijving

From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications.



  • Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems.
  • Offers potential applications to the analysis and control of new dimension-varying systems.
  • Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.

Details

Titel: Mathematics in Science and Engineering, From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
auteur: Cheng, Daizhan
Mediatype: Boek
Bindwijze: Paperback
Taal: Engels
Aantal pagina's: 364
Uitgever: Elsevier Science
Publicatiedatum: 2019-05-21
NUR: Toepassingsgerichte wiskunde
Afmetingen: 229 x 152
ISBN/ISBN13: 9780128178010
Intern nummer: 43503280

Biografie (woord)

Daizhan Cheng is the creator of the novel and highly-useful product of matrices called the semi-tensor product (STP) or Cheng product. He holds a PhD from Washington University, St. Louis, and since 1990, he has served as a professor with the Institute of Systems Science, AMSS, Chinese Academy of Sciences. He is the author / co-author of 14 books, over 250 journal papers, and more than 150 conference papers. He received the Second National Natural Science Award in both 2008 and 2014, the Outstanding Science and Technology Achievement Price of CAS in 2015, and the Automatica Best Paper Award (2008 2010), bestowed by the IFAC.

Extra informatie

Delivers a masterful exposition of semi-tensor product with potential applications to analysis and control of new dimension-varying systems.

Quote

"Dimension-free matrix theory and the cross-dimensional dynamic system theory presented in this book may be useful tools to handle and even model dimension-varying systems. The intended application areas are (i) genetic regulatory networks, where cells may die or be born at any time; (ii) the internet or some other service-based networks, where some users may join in or withdraw from time to time; (iii) some engineering applications, the modeling of spacecraft systems and vehicle clutch systems; etc. The results in the book are new. This book starts a new direction for further study." --Mathematical Reviews Clippings

Inhoudsopgave

1. Semi-tensor product of matrices 2. Boolean networks 3. Finite games 4. Equivalence and lattice structures 5. Topological structure on quotient space 6. Differential geometry on set of matrices 7. Cross-dimensional Lie algebra and Lie group 8. Second matrix-matrix semi-tensor product 9. Structure on set of vectors 10. Dimension-varying linear system 11. Dimension-varying linear control system 12. Generalized dynamic systems 13. Dimension-varying nonlinear dynamic systems A. Mathematical preliminaries

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