Matrices in ACL2

This paper describes some initial work on a formalization of matrices in ACL2. The current work is focused on creating an executable implementation that is simple to mechanically reason with and complete enough to be capable of analyzing real problems in linear algebra. A number of basic operations have been defined including matrix addition, transposition and multiplication by a scalar, a vector, and another matrix. These operations have an extensive library of over 200 theorems to make reasoning about these operations more convenient and automatic. These theorems include the axioms for rings and other rewrite rules that attempt to change matrix expressions into a canonical form. Unlike the work in [2] where the focus was mainly on implementing Strassens algorithm for square matrices where the number of rows and columns is a power of 2, this operations are for arbitrary m × n matrices. This paper is intended to be a brief introduction to the matrix library. It is not intended as a reference, and for detailed questions there is no substitute for consulting the source code of the books directly. Hopefully after reading this paper, navigating those books will be easier.