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Integer Factorization of a Positive-Definite Matrix

Integer factorization of a positive-definite matrix
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2015 United States English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 29, pages 1,783-1,791 (issn: 0895-4801, eissn: 1095-7146, Copyright policy )
Authors: Tropp, Joel A.;

doi: 10.1137/15m1024718 , 10.48550/arxiv.1506.00340

arXiv: 1506.00340

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

Country
United States
Related Organizations
Keywords

positive definite matrix, convex geometry, discrete geometry, outer product, Metric Geometry (math.MG), matrix factorization, Factorization of matrices, 52A99, 52C99, 510, Conditioning of matrices, Positive matrices and their generalizations; cones of matrices, geometric mean, Mathematics - Metric Geometry, Multilinear algebra, tensor calculus, FOS: Mathematics, conic geometry, positive-definite matrix, condition number

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    		 4
    popularity
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    influence
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    impulse
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
Average
Green
bronze