Spectral Methods for Matrix Rigidity with Applications to Size-Depth Trade-offs and Communication Complexity

@article{Lokam2001SpectralMF,
  title={Spectral Methods for Matrix Rigidity with Applications to Size-Depth Trade-offs and Communication Complexity},
  author={Satyanarayana V. Lokam},
  journal={J. Comput. Syst. Sci.},
  year={2001},
  volume={63},
  pages={449-473}
}
The rigidity of a matrix measures the number of entries that must be changed in order to reduce its rank below a certain value. The known lower bounds on the rigidity of explicit matrices are very weak. It is known that stronger lower bounds would have important consequences in complexity theory. We consider some restricted variants of the rigidity problem over the complex numbers. Using spectral methods, we derive lower bounds on these variants. Two applications of such restricted variants are… CONTINUE READING

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