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.
https://hal.inria.fr/hal-01383331 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Tuesday, October 18, 2016 - 2:55:39 PM Last modification on : Wednesday, October 13, 2021 - 7:16:03 PM
Liming Li, Zhiping Shi, Yong Guan, Jie Zhang, Hongxing Wei. Formalizing the Matrix Inversion Based on the Adjugate Matrix in HOL4. 8th International Conference on Intelligent Information Processing (IIP), Oct 2014, Hangzhou, China. pp.178-186, ⟨10.1007/978-3-662-44980-6_20⟩. ⟨hal-01383331⟩