From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
- 1st Edition - May 18, 2019
- Latest edition
- Author: Daizhan Cheng
- Language: English
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that exte… Read more
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.
- Provides, for the first time, cross-dimensional system theory that is useful for modeling 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.
Upper-division undergraduates, graduate students, and researchers worldwide working in mathematics, economics, and engineering
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
- Edition: 1
- Latest edition
- Published: May 18, 2019
- Language: English
DC