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.
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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
