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From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
Daizhan Cheng
出版Academic Press, 2019-05-18
主題Mathematics / Applied
ISBN01281780279780128178027
URLhttp://books.google.com.hk/books?id=cA6ZDwAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.