Matrix rigidity of random Toeplitz matrices

  title={Matrix rigidity of random Toeplitz matrices},
  author={Oded Goldreich and Avishay Tal},
  journal={computational complexity},
A matrix A is said to have rigidity s for rank r if A differs from any matrix of rank r on more than s entries. We prove that random n-by-n Toeplitz matrices over $${\mathbb{F}_{2}}$$ F2 (i.e., matrices of the form $${A_{i,j} = a_{i-j}}$$ Ai,j=ai-j for random bits $${a_{-(n-1)}, \ldots, a_{n-1}}$$ a-(n-1),…,an-1 ) have rigidity $${\Omega(n^3/(r^2\log n))}$$ Ω(n3/(r2logn)) for rank $${r \ge \sqrt{n}}$$ r≥n , with high probability. This improves, for $${r = o(n/\log n \log\log n)}$$ r=o(n… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 17 references

A note on matrix rigidity

  • J. Friedman
  • Combinatorica
  • 1993
Highly Influential
3 Excerpts

Complexity Lower Bounds using Linear Algebra

  • S. V. Lokam
  • Foundations and Trends in Theoretical Computer…
  • 2009
1 Excerpt

Similar Papers

Loading similar papers…