English

Integer factorization of a positive-definite matrix

Metric Geometry 2015-08-05 v3

Abstract

This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension of the matrix.

Keywords

Cite

@article{arxiv.1506.00340,
  title  = {Integer factorization of a positive-definite matrix},
  author = {Joel A. Tropp},
  journal= {arXiv preprint arXiv:1506.00340},
  year   = {2015}
}

Comments

7 pages. v2: Change to the title. Corrects several errors and the example that justifies the optimality of the main result. v3: More small errors corrected

R2 v1 2026-06-22T09:44:44.250Z