Archive for Mathematical Logic

, Volume 51, Issue 5, pp 535–551

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

Authors

Article

DOI: 10.1007/s00153-012-0280-0

Cite this article as:
Soltys, M. Arch. Math. Logic (2012) 51: 535. doi:10.1007/s00153-012-0280-0

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 complexitymatrix identitiesFrege and extended Frege

Mathematical Subject Classification

15

Copyright information

© Springer-Verlag 2012