A Formalization of Elementary Linear Algebra: Part II
David Russinoff
TL;DR
This paper extends a formal ACL2 framework for elementary linear algebra, focusing on matrices over a field, including row reduction, matrix inversion, and solving linear systems.
Contribution
It introduces formal proofs of elementary row operations, matrix inverses, and solutions for linear systems over fields within ACL2, building on previous matrix algebra formalization.
Findings
Formal proof of elementary row reduction over fields
Verified algorithms for matrix inversion
Automated solutions for linear systems
Abstract
This is the second installment of an exposition of an ACL2 formalization of elementary linear algebra. It extends the results of Part I, which covers the algebra of matrices over a commutative ring, but focuses on aspects of the theory that apply only to matrices over a field: elementary row reduction and its application to the computation of matrix inverses and the solution of simultaneous systems of linear equations.
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