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Formalizing the matrix inversion based on the adjugate matrix in HOL4

  • Liming Li
  • , Zhiping Shi*
  • , Yong Guan
  • , Jie Zhang
  • , Hongxing Wei
  • *Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper presents the formalization of the matrix inversion based on the adjugate matrix in the HOL4 system. It is very complex and difficult to formalize the adjugate matrix, which is composed of matrix cofactors. Because HOL4 is based on a simple type theory, it is difficult to formally express the sub-matrices and cofactors of an n-by-n matrix. In this paper, special n-by-n matrices are constructed to replace the (n - 1)-by-(n - 1) sub-matrices, in order to compute the cofactors, thereby, making it possible to formally construct aadjugate matrices. The Laplace’s formula is proven and the matrix inversion based on the adjugate matrix is then inferred in HOL4. The paper also presents formal proofs of properties of the invertible matrix.

Original languageEnglish
Title of host publicationIntelligent Information Processing VII - 8th IFIP TC 12 International Conference, IIP 2014, Proceedings
EditorsDavid Leake, Uli Sattler, Zhongzhi Shi, Zhaohui Wu
PublisherSpringer New York LLC
Pages178-186
Number of pages9
ISBN (Electronic)9783662449790
StatePublished - 2014
Event8th IFIP International Conference on Intelligent Information Processing, IIP 2014 - Hangzhou, China
Duration: 17 Oct 201420 Oct 2014

Publication series

NameIFIP Advances in Information and Communication Technology
Volume432
ISSN (Print)1868-4238

Conference

Conference8th IFIP International Conference on Intelligent Information Processing, IIP 2014
Country/TerritoryChina
CityHangzhou
Period17/10/1420/10/14

Keywords

  • Adjugate matrix
  • Formal verification
  • HOL4
  • Matrix inversion
  • Theorem proving

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