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: 1st June 2019
Page Count: 350
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Table of Contents

1. Semi-tensor Product of Matrices
2. Boolean Networks
3. Finite Games
4. M-equivalence and Lattice Structure
5. Semi-Group Structure of Matrices
6. Lattice of Matrix Subspaces
7. Quotient Space and Vector Space Structure
8. Topology on Mμ and Σμ
9. Metric on Σμ
10. Manifold Structure and Functions on Σμ
11. Differential Geometry on Σμ
12. Ring Structure on M-equivalent Square Matrices
13. Lie Algebra on Σ1
14. Lie Group on Σ1
15. Dimension-Free Vector Space
16. Quotient Vector Space
17. Cross-Dimensional Projection
18. Cross-dimensional Dynamic System
19. Invariant Subspace
20. Formal Polynomial of Matrices
21. Cross-Dimensional Linear System
22. Cross-Dimensional Linear Control System
23. Dynamic and Control Systems on Quotient Space
24. Finite Dimensional Projective Realization
25. PM as a Vector Space on M
26. Discrete-time Cross-Dimensional Nonlinear Systems
27. Continuous-time Cross-Dimensional Nonlinear Systems A Mathematical Preliminaries


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. Dimension-varying systems are everywhere, and through innovative applications its 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 useful for modelling some 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.


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


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    © Academic Press 2019
    Academic Press
    Paperback ISBN:

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    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

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