From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems


Download From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems written by Daizhan Cheng in PDF format. This book is under the category Mathematics and bearing the isbn/isbn13 number 0128178019; 0128178027/9780128178010/ 9780128178027. You may reffer the table below for additional details of the book.


From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems; (PDF) displays the first arithmetic of semi-tensor product (STP); a generalized matrix product that extends the traditional matrix product to two matrices of arbitrary dimensions. Dimension-varying techniques include prominently throughout many disciplines; and thru progressive functions; its newly developed idea can rework giant knowledge techniques corresponding to genomics and biosystems; IT; deep studying; and knowledge-based mostly engineering functions.

  • Provides potential functions to the evaluation and management of recent dimension-various techniques.
  • Offers; for the primary time; cross-dimensional system idea that’s helpful for modeling dimension-various techniques.
  • Explores the underlying arithmetic of semi-tensor product; together with the equivalence and lattice construction of matrices and monoid of matrices with arbitrary dimensions.


Dimension-free matrix theory and the cross-dimensional dynamic system theory presented in this ebook may be useful tools to manage and even model dimension-varying systems. The aimed application areas are (i) genetic regulatory networks; where cells may die or be born at any time; (ii) some engineering applications; the modeling of spacecraft systems and vehicle clutch systems; (iii) the internet or some other service-based networks; where some users may join in or withdraw from time to time; etc. The results in the ebook are new. This ebook starts a new direction for further study.” — Mathematical Reviews Clippings

NOTE: The product solely consists of the ebook; From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems in PDF. No access codes are included.

Additional information


Daizhan Cheng


Academic Press; 1st edition










0128178019; 0128178027


9780128178010/ 9780128178027

Table of contents

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

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