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Formalization of Matrix Theory in HOL4
Advances in Mechanical Engineering
  • Zhiping Shi, Chinese Academy of Sciences
  • Yan Zhang, Capital Normal University
  • Zhenke Liu, Capital Normal University
  • Xinan Kang, Capital Normal University
  • Yong Guan, Capital Normal University
  • Jie Zhang, Beijing University of Chemical Technology
  • Xiaoyu Song, Portland State University
Document Type
Publication Date
  • Matrices,
  • Number theory,
  • Dynamical systems,
  • Vector fields
Matrix theory plays an important role in modeling linear systems in engineering and science. To model and analyze the intricate behavior of complex systems, it is imperative to formalize matrix theory in a metalogic setting. This paper presents the higherorder logic (HOL) formalization of the vector space and matrix theory in the HOL4 theorem proving system. Formalized theories include formal definitions of real vectors and matrices, algebraic properties, and determinants, which are verified in HOL4. Two case studies, modeling and verifying composite two-port networks and state transfer equations, are presented to demonstrate the applicability and effectiveness of our work.

Copyright © 2014 Zhiping Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Shi, Z., Zhang, Y., Liu, Z., Kang, X., Guan, Y., Zhang, J., & Song, X. (2014). Formalization of matrix theory in HOL4. Advances in Mechanical Engineering, 6, 195276.