Smallest singular value of sparse random matrices

• Author / Creator

  Rivasplata, Omar D

• In this thesis probability estimates on the smallest singular value of random matrices with independent entries are extended to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix, and help to clarify the role of the variances in the corresponding estimates. We also show that it is enough to require boundedness from above of the r-th moment of the entries, for some r > 2.

• Subjects / Keywords

  • Singular values
  • Sparse matrices
  • Sub-Gaussian random variables
  • Deviation inequalities
  • Incompressible vectors
  • Compressible vectors
  • Invertibility of random matrices
  • Random matrices

• Graduation date

  Spring 2012

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3FQ04

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.