1. Formalizing the Matrix Inversion Based on the Adjugate Matrix in HOL4
- Author
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Jie Zhang, Hongxing Wei, Li Liming, Yong Guan, Zhiping Shi, Capital Normal University [Beijing], Beijing University of Chemical Technology, Beihang University (BUAA), Zhongzhi Shi, Zhaohui Wu, David Leake, Uli Sattler, and TC 12
- Subjects
Adjugate matrix ,Hollow matrix ,Computer science ,Matrix inversion ,010102 general mathematics ,Minor (linear algebra) ,MathematicsofComputing_NUMERICALANALYSIS ,Block matrix ,0102 computer and information sciences ,Single-entry matrix ,HOL4 ,01 natural sciences ,law.invention ,Algebra ,Formal verification ,Invertible matrix ,010201 computation theory & mathematics ,law ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,[INFO]Computer Science [cs] ,Nonnegative matrix ,0101 mathematics ,Centrosymmetric matrix ,Theorem proving - Abstract
Part 5: Automatic Reasoning; International audience; 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.
- Published
- 2014
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