From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
  • Author : Daizhan Cheng
  • Release Date : 18 May 2019
  • Publisher : Academic Press
  • Genre : Mathematics
  • Pages : 364
  • ISBN 13 : 9780128178027

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Book excerpt: 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.

From Dimension Free Matrix Theory to Cross Dimensional Dynamic Systems

From Dimension Free Matrix Theory to Cross Dimensional Dynamic Systems

Author : Daizhan Cheng
Publisher : Academic Press
Genre : Mathematics
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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 ...

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Author : Ralph Abraham,Laura Gardini,C. Mira
Publisher : Springer Science & Business Media
Genre : Computers
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Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the ...

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Author : Ramin S. Esfandiari,Bei Lu
Publisher : CRC Press
Genre : Technology & Engineering
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Modeling and Analysis of Dynamic Systems, Third Edition introduces MATLAB®, Simulink®, and SimscapeTM and then utilizes them to perform symbolic, graphical, numerical, and simulation tasks. Written for senior level courses/modules, the textbook meticulously covers techniques for modeling a variety of engineering systems, methods of response analysis, and introductions to ...

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Author : Cornelius T. Leondes
Publisher : Routledge
Genre : Mathematics
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The finite element, an approximation method for solving differential equations of mathematical physics, is a highly effective technique in the analysis and design, or synthesis, of structural dynamic systems. Starting from the system differential equations and its boundary conditions, what is referred to as a weak form of the problem (...

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Author : Abraham Berman,Michael Neumann,Robert J. Plemmons,Ronald J. Stern
Publisher : Wiley-Interscience
Genre : Mathematics
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This work applies the theory of nonnegative matrices to problems arising in positive differential and control systems. There is a concise review of requisite material in convex analysis and matrix theory, as well as a detailed review of linear differential and control systems. Exposition incorporates simple real-world dynamic models to ...

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Publisher : John Wiley & Sons Incorporated
Genre : Science
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Difference and differential equations; Linear algebra; Linear state equations; Linear systems with constant coefficients; Positive systems; Markov chains; Concepts of control; Analysis of nonlinear systems; Some important dynamic systems; Optimal control....

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Author : László Erdős,Horng-Tzer Yau
Publisher : American Mathematical Soc.
Genre : Random matrices
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A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses ...

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Author : Thomas Heinzeller,James H. Nebelsick
Publisher : CRC Press
Genre : Science
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Since 1972, scientists from all over the world working on fundamental questions of echinoderm biology and palaeontology have conferred every three years to exchange current views and results. The 11th International Echinoderm Conference held at the University of Munich, Germany, from 6-10 October 2003,continued this tradition. This volume comprises 95 submitted papers ...