Abstract: 
We provide the operations of matrix addition, multiplication,
transposition, and matrix comparisons as executable functions over
ordered semirings. Moreover, it is proven that strongly normalizing
(monotone) orders can be lifted to strongly normalizing (monotone) orders
over matrices. We further show that the standard semirings over the
naturals, integers, and rationals, as well as the arctic semirings
satisfy the axioms that are required by our matrix theory. Our
formalization is part of the CeTA system
which contains several termination techniques. The provided theories have
been essential to formalize matrixinterpretations and arctic
interpretations.

BibTeX: 
@article{MatrixAFP,
author = {Christian Sternagel and RenĂ© Thiemann},
title = {Executable Matrix Operations on Matrices of Arbitrary Dimensions},
journal = {Archive of Formal Proofs},
month = jun,
year = 2010,
note = {\url{http://isaafp.org/entries/Matrix.shtml},
Formal proof development},
ISSN = {2150914x},
}
