Integer Factorization of a Positive-Definite Matrix
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.
© 2015 by Society for Industrial and Applied Mathematics. Received by the editors June 8, 2015; accepted for publication (in revised form) August 12, 2015; published electronically October 1, 2015. This work was supported by ONR award N00014-11-1002 and the Gordon and Betty Moore Foundation.
Submitted - 1506.00340v3.pdf
Published - 15m1024718.pdf