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

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 A. Mathematical preliminaries

Authors

Daizhan Cheng Institute of Systems Science, AMSS, Chinese Academy of Sciences, China. 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.