From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
Published on 21. May 2019
Book
Paperback/Softback
364 pages
978-0-12-817801-0 (ISBN)
Description
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a 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 learning, IT, and information-based engineering applications.
Reviews / Votes
"Dimension-free matrix theory and the cross-dimensional dynamic system theory presented in this book may be useful tools to handle and even model dimension-varying systems. The intended application areas are (i) genetic regulatory networks, where cells may die or be born at any time; (ii) the internet or some other service-based networks, where some users may join in or withdraw from time to time; (iii) some engineering applications, the modeling of spacecraft systems and vehicle clutch systems; etc. The results in the book are new. This book starts a new direction for further study." --Mathematical Reviews ClippingsMore details
Series
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
Professional and scholarly
Upper-division undergraduates, graduate students, and researchers worldwide working in mathematics, economics, and engineering
Product notice
Paperback (trade)
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 19 mm
Weight
488 gr
ISBN-13
978-0-12-817801-0 (9780128178010)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
05/2019
Academic Press
€131.00
Available for download
Person
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.
Content
1. Semi-tensor product of matrices2. Boolean networks3. Finite games4. Equivalence and lattice structures5. Topological structure on quotient space6. Differential geometry on set of matrices7. Cross-dimensional Lie algebra and Lie group8. Second matrix-matrix semi-tensor product9. Structure on set of vectors10. Dimension-varying linear system11. Dimension-varying linear control system12. Generalized dynamic systems13. Dimension-varying nonlinear dynamic systemsA. Mathematical preliminaries