# Executable Matrix Operations on Matrices of Arbitrary Dimensions

 Title: Executable Matrix Operations on Matrices of Arbitrary Dimensions Authors: Christian Sternagel (c /dot/ sternagel /at/ gmail /dot/ com) and René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at) Submission date: 2010-06-17 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 matrix-interpretations and arctic interpretations. Change history: [2010-09-17]: Moved theory on arbitrary (ordered) semirings to Abstract Rewriting. BibTeX: @article{Matrix-AFP, author = {Christian Sternagel and René Thiemann}, title = {Executable Matrix Operations on Matrices of Arbitrary Dimensions}, journal = {Archive of Formal Proofs}, month = jun, year = 2010, note = {\url{https://isa-afp.org/entries/Matrix.html}, Formal proof development}, ISSN = {2150-914x}, } License: GNU Lesser General Public License (LGPL) Depends on: Abstract-Rewriting Used by: Knuth_Bendix_Order, Matrix_Tensor, Polynomials, Transitive-Closure Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.