内容简介：　　　

　　 From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product(STP), a novel 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 leaning. IT, and information-based engineering applications. This book ia an ideal reference for researchers, graduate students and practitioners working in the fields of mathematics, economics and engineering.

Key Features:
　　 Provides, for the first time, cross-dimensional system theory useful for modeling some 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.

About the 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 holds a PhD from Washington University, St. Louis, and since 1990, he has served ad 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 Mational Natural Science Award in both 2008 and 2014, the Outstanding Science and Technology Achievement Prize of CAS in 2015, and the Automatica Best Paper Award (2008-2010), bestowed by the IFAC.

英文目录：
Contents
Chapter 0: Preface
Chapter 1: Semi-tensor product of matrices
Chapter 2: Boolean networks
Chapter 3: Finite games
Chapter 4: Equivalence and lattice structures
Chapter 5: Topological structure on quotient space
Chapter 6: Differential geometry on set of matrices
Chapter 7: Cross-dimensional Lie algebra and Lie group
Chapter 8: Second matrix-matrix semi-tensor product
Chapter 9: Structure on set of vectors
Chapter 10: Dimension-varying linear system
Chapter 11: Dimension-varying linear control system
Chapter 12: Generalized dynamic systems
Chapter 13: Dimension-varying nonlinear dynamic systems
Appendix: Mathematical preliminaries