Synopses & Reviews
Synopsis
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product, a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems are everywhere, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and bio-systems, deep learning, IT, and information-based engineering applications.
- Offers potential applications to the analysis and control of new dimension-varying systems.
- Provides for the first time cross-dimensional system theory useful for modelling some dimension-varying systems.
- Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid (semi-group with identity) of matrices with arbitrary dimensions.