From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
| By: | Daizhan Cheng |
| Publisher: | Elsevier S & T |
| Print ISBN: | 9780128178010 |
| eText ISBN: | 9780128178027 |
| Edition: | 0 |
| Copyright: | 2019 |
| Format: | Page Fidelity |
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Table of Contents
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.