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

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. Dimension-varying systems are everywhere, and through innovative applications its 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 useful for modelling some dimension-varying systemsIncludes a brand new dimension-free matrix theory and cross-dimensional dynamic system theoryInvestigates 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 INDICE: 1. Semi-tensor Product of Matrices 2. Boolean Networks 3. Finite Games 4. M-equivalence and Lattice Structure 5. Semi-Group Structure of Matrices 6. Lattice of Matrix Subspaces 7. Quotient Space and Vector Space Structure 8. Topology on M? and ?? 9. Metric on ?? 10. Manifold Structure and Functions on ?? 11. Differential Geometry on ?? 12. Ring Structure on M-equivalent Square Matrices 13. Lie Algebra on ?1 14. Lie Group on ?1 15. Dimension-Free Vector Space 16. Quotient Vector Space 17. Cross-Dimensional Projection 18. Cross-dimensional Dynamic System 19. Invariant Subspace 20. Formal Polynomial of Matrices 21. Cross-Dimensional Linear System 22. Cross-Dimensional Linear Control System 23. Dynamic and Control Systems on Quotient Space 24. Finite Dimensional Projective Realization 25. PM as a Vector Space on M 26. Discrete-time Cross-Dimensional Nonlinear Systems 27. Continuous-time Cross-Dimensional Nonlinear Systems A Mathematical Preliminaries

• ISBN: 978-0-12-817801-0
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 350
• Fecha Publicación: 01/06/2019
• Nº Volúmenes: 1
• Idioma: Inglés