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