Dynamic Matrix Rank

  • Gudmund Skovbjerg Frandsen
  • Peter Frands Frandsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


We consider maintaining information about the rank of a matrix under changes of the entries. For n×n matrices, we show an upper bound of O(n 1.575) arithmetic operations and a lower bound of Ω(n) arithmetic operations per change. The upper bound is valid when changing up to O(n 0.575) entries in a single column of the matrix. Both bounds appear to be the first non-trivial bounds for the problem. The upper bound is valid for arbitrary fields, whereas the lower bound is valid for algebraically closed fields. The upper bound uses fast rectangular matrix multiplication, and the lower bound involves further development of an earlier technique for proving lower bounds for dynamic computation of rational functions.


Arithmetic Operation Computation Tree Implicit Representation Dynamic Matrix Dynamic Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gudmund Skovbjerg Frandsen
    • 1
  • Peter Frands Frandsen
    • 2
  1. 1.BRICSUniversity of AarhusDenmark
  2. 2.Rambøll ManagementAarhusDenmark

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