From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems

ISBN: 9780128178010 出版年：2019 页码：366 Cheng, Daizhan Academic Press_RM

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.