Skip to main content
SpringerLink
Log in

A fast parallel algorithm to compute the rank of a matrix over an arbitrary field

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

It is shown that the rank of a matrix over an arbitrary field can be computed inO(log2 n) time using a polynomial number of processors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Berkowitz, On computing the determinant in small parallel time using a small number of processors,Inform. Process. Lett.,18 (1984), 147–150.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Borodin, S. A. Cook andN. Pippenger, Parallel computation for well-endowed rings and space bounded probabilistic machines,Information and Control 58 (1983), 113–136.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Borodin, J. von zur Gathen andJ. Hopcroft, Fast parallel matrix and GCD computations,Information and Control,52 (1982), 241–256.

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Csánky, Fast parallel matrix inversion algorithms,SIAM J. Comput.,5 (1976).

  5. J. von zur Gathen, private communication.

  6. O. Ibarra, S. Moran andL. E. Rosier, A note on the parallel complexity of computing the rank of ordern matrices,Information Processing Letters,11 (1980), 162.

    Article  MathSciNet  Google Scholar 

  7. E. M. Luks andP. McKenzie, Fast parallel computation with permutation groups,Proc. 25 th FOCS, 1985, 505–514.

  8. P. McKenzie andS. A. Cook, The parallel complexity of the abelian permutation group membership,Proc. 24 th FOCS, 1983, 154–161.

Download references

Author information

Authors and Affiliations

  1. EECS Department, Computer Sci. Division, University of California, 94720, Berkeley, CA, USA

    Ketan Mulmuley

Authors
  1. Ketan Mulmuley
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Also appeared in ACM Symposium on Theory of Computing, May 28–30, 1986 Berkeley, California. Research supported by Miller Fellowship, University of California, Berkeley.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mulmuley, K. A fast parallel algorithm to compute the rank of a matrix over an arbitrary field. Combinatorica 7, 101–104 (1987). https://doi.org/10.1007/BF02579205

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579205

AMS subject classification (1980)

Search

Navigation