- Research Article
- Open Access
Linear Maps which Preserve or Strongly Preserve Weak Majorization
- Ahmad Mohammad Hasani1Email author and
- Mohammad Ali Vali1
https://doi.org/10.1155/2007/82910
© A. M. Hasani and M. A. Vali 2007
Received: 8 July 2007
Accepted: 5 November 2007
Published: 6 February 2008
Abstract
For
, we say
is weakly submajorized (weakly supermajorized) by
, and write
, if
, where
denotes the
th component of the vector
whose components are a decreasing (increasing) rearrangment of the components of
. We characterize the linear maps that preserve (strongly preserve) one of the majorizations
or
.
Keywords
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This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
