Nonnegativity Preservation under Singular Values Perturbation

Emedin Montaño, Mario Salas and Ricardo L. Soto

Mathematical Problems in Engineering, 2009, vol. 2009, 1-25

Abstract:

We study how singular values and singular vectors of a matrix ð ´ change, under matrix perturbations of the form ð ´ + ð ›¼ ð ® ð ‘– ð ¯ âˆ— ð ‘– and ð ´ + ð ›¼ ð ® ð ‘ ð ¯ âˆ— ð ‘ž , ð ‘ â‰ ð ‘ž , where ð ›¼ ∈ â„ , ð ´ is an ð ‘š × ð ‘› positive matrix with singular values 𠜎 1 ≥ 𠜎 2 ≥ ⋯ ≥ 𠜎 ð ‘Ÿ > 0 , ð ‘Ÿ = m i n { ð ‘š , ð ‘› } , and ð ® ð ‘— , ð ¯ ð ‘˜ , ð ‘— = 1 , … , ð ‘š ; 𠑘 = 1 , … , ð ‘› , are the left and right singular vectors, respectively. In particular we give conditions under which this kind of perturbations preserve nonnegativity and certain matrix structures.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:301582

DOI: 10.1155/2009/301582

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