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From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems de Daizhan Cheng

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

Autor Daizhan Cheng
en Limba Engleză Paperback – 21 mai 2019
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.
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Specificații

ISBN-13: 9780128178010
ISBN-10: 0128178019
Pagini: 364
Dimensiuni: 152 x 229 x 25 mm
Greutate: 0.49 kg
Editura: ELSEVIER SCIENCE
Seria Mathematics in Science and Engineering

Public țintă

Upper-division undergraduates, graduate students, and researchers worldwide working in mathematics, economics, and engineering

Cuprins

1. Semi-tensor product of matrices2. Boolean networks3. Finite games4. Equivalence and lattice structures5. Topological structure on quotient space6. Differential geometry on set of matrices7. Cross-dimensional Lie algebra and Lie group8. Second matrix-matrix semi-tensor product9. Structure on set of vectors10. Dimension-varying linear system11. Dimension-varying linear control system12. Generalized dynamic systems13. Dimension-varying nonlinear dynamic systemsA. Mathematical preliminaries

Recenzii

"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