From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems – eBook PDF
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems, (PDF) reflects the primary 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 include prominently across many disciplines, and through innovative applications, its newly developed theory can transform large data systems such as genomics and biosystems, IT, deep learning, and information-based engineering applications.
- Provides potential applications to the analysis and control of new dimension-varying systems.
- Offers, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems.
- Explores the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.
“Dimension-free matrix theory and the cross-dimensional dynamic system theory presented in this ebook may be useful tools to manage and even model dimension-varying systems. The aimed application areas are (i) genetic regulatory networks, where cells may die or be born at any time; (ii) some engineering applications, the modeling of spacecraft systems and vehicle clutch systems; (iii) the internet or some other service-based networks, where some users may join in or withdraw from time to time; etc. The results in the ebook are new. This ebook starts a new direction for further study.” — Mathematical Reviews Clippings
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