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

Nonfiction, Science & Nature, Mathematics, Applied
Cover of the book From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems by Daizhan Cheng, Elsevier Science
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Author: Daizhan Cheng ISBN: 9780128178027
Publisher: Elsevier Science Publication: May 18, 2019
Imprint: Academic Press Language: English
Author: Daizhan Cheng
ISBN: 9780128178027
Publisher: Elsevier Science
Publication: May 18, 2019
Imprint: Academic Press
Language: English

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.
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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.

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