Integer Factorization of a Positive-Definite Matrix
Copyright policy )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.
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
- California Institute of Technology United States
convex geometry, discrete geometry, Metric Geometry (math.MG), matrix factorization, 52A99, 52C99, 510, Mathematics - Metric Geometry, FOS: Mathematics, conic geometry, positive-definite matrix
convex geometry, discrete geometry, Metric Geometry (math.MG), matrix factorization, 52A99, 52C99, 510, Mathematics - Metric Geometry, FOS: Mathematics, conic geometry, positive-definite matrix
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