From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems - 1st Edition - ISBN: 9780128178010

From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems

1st Edition

Authors: Daizhan Cheng
Paperback ISBN: 9780128178010
Imprint: Academic Press
Published Date: 31st May 2019
Page Count: 364
Sales tax will be calculated at check-out Price includes VAT/GST

Institutional Subscription

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Table of Contents

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


Description

From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product, a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. As dimension-varying systems are everywhere, this newly developed theory can revolutionize large data systems, such as genomics and bio-systems, deep learning, IT and information-based engineering applications.

Key Features

  • Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems
  • Includes a brand new dimension-free matrix theory and cross-dimensional dynamic system theory
  • Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid (semi-group with identity) of matrices with arbitrary dimensions

Readership

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


Details

No. of pages:
364
Language:
English
Copyright:
© Academic Press 2019
Published:
Imprint:
Academic Press
Paperback ISBN:
9780128178010

Ratings and Reviews


About the Authors

Daizhan Cheng Author

Daizhan Cheng is the creator of the novel and highly-useful product of matrices called the semi-tensor product (STP) or Cheng product. He graduated from Tsinghua University in 1970, received M.S. from Graduate School, Chinese Academy of Sciences in 1981, and Ph.D. from Washington University, St. Louis, in 1985. Since 1990, he has served as a professor with the Institute of Systems Science, AMSS, Chinese Academy of Sciences. He is the author/coauthor of 14 books, over 250 journal papers, and over 150 conference papers. He was a member of IEEE CSS Board of Governors (2009, 2015) and the IFAC Council (2011-2014). He is an IEEE Fellow (2006-) and IFAC Fellow (2008-). He twice received the Second National Natural Science Award (in 2008 and 1014), the Outstanding Science and Technology Achievement Price of CAS (2015), and the Automatica Best Paper Award (2008-2010), bestowed by the IFAC.

Affiliations and Expertise

Institute of Systems Science, AMSS, Chinese Academy of Sciences, China