Matrix Operations

swMATH ID: 28791
Software Authors: Christian Sternagel; René Thiemann
Description: Executable Matrix Operations on Matrices of Arbitrary Dimensions, 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.
Homepage: https://www.isa-afp.org/entries/Matrix.html
Dependencies: Isabelle
Related Software: Archive Formal Proofs; Lifting; Transfer; OpenGeoProver; CeTA; Isar; Isabelle/HOL
Referenced in: 1 Publication

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