Archive for Mathematical Logic

, Volume 44, Issue 2, pp 195–208 | Cite as

Weak theories of linear algebra

Article

Abstract.

We investigate the theories Open image in new window of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize Frege proofs. We give sentences separating quantified versions of these theories, and define a fragment Open image in new window in which we can interpret a weak theory V1 of bounded arithmetic and carry out polynomial time reasoning about matrices - for example, we can formalize the Gaussian elimination algorithm. We show that, even if we restrict our language, Open image in new window proves the commutativity of inverses.

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Notes

Acknowledgments.

The authors would like to thank Steve Cook for the very helpful conversations that led to this work.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.St Hilda’s CollegeOxfordUK
  2. 2.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada

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