Integer factorization of a positive-definite matrix

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.

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