Archive for Mathematical Logic

, Volume 51, Issue 5–6, pp 535–551 | Cite as

Proving properties of matrices over \({\mathbb{Z}_{2}}\)

Article

Abstract

We prove assorted properties of matrices over \({\mathbb{Z}_{2}}\), and outline the complexity of the concepts required to prove these properties. The goal of this line of research is to establish the proof complexity of matrix algebra. It also presents a different approach to linear algebra: one that is formal, consisting in algebraic manipulations according to the axioms of a ring, rather than the traditional semantic approach via linear transformations.

Keywords

Proof complexity matrix identities Frege and extended Frege 

Mathematical Subject Classification

15 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.McMaster UniversityHamiltonCanada

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