The proof complexity of linear algebra. Soltys, M. & Cook, S. A. Ann. Pure Appl. Logic (APAL), 130(1-3):277-323, 2004.
The proof complexity of linear algebra [link]Paper  bibtex   
@article{ dblp3236506,
  title = {The proof complexity of linear algebra},
  author = {Michael Soltys and Stephen A. Cook},
  author_short = {Soltys, M. and Cook, S. A.},
  bibtype = {article},
  type = {article},
  year = {2004},
  key = {dblp3236506},
  id = {dblp3236506},
  biburl = {http://www.dblp.org/rec/bibtex/journals/apal/SoltysC04},
  url = {http://dx.doi.org/10.1016/j.apal.2003.10.018},
  journal = {Ann. Pure Appl. Logic (APAL)},
  pages = {277-323},
  number = {1-3},
  volume = {130},
  text = {Ann. Pure Appl. Logic (APAL) 130(1-3):277-323 (2004)}
}

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