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.
Author(s): Daizhan Cheng
Series: Mathematics in Science and Engineering
Publisher: Academic Press
Year: 2019
Language: English
Pages: 353
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
