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.
- 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
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
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.