Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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STRONG PRESERVERS OF SYMMETRIC ARCTIC RANK OF NONNEGATIVE REAL MATRICES

  • Beasley, LeRoy B. (Department of Mathematics and Statistics Utah State University) ;
  • Encinas, Luis Hernandez (Institute of Physical and Information Technologies Spanish National Research Council (CSIC)) ;
  • Song, Seok-Zun (Department of Mathematics Jeju National University)
  • Received : 2018.11.11
  • Accepted : 2019.02.07
  • Published : 2019.11.01
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Abstract

A rank 1 matrix has a factorization as $uv^t$ for vectors u and v of some orders. The arctic rank of a rank 1 matrix is the half number of nonzero entries in u and v. A matrix of rank k can be expressed as the sum of k rank 1 matrices, a rank 1 decomposition. The arctic rank of a matrix A of rank k is the minimum of the sums of arctic ranks of the rank 1 matrices over all rank 1 decomposition of A. In this paper we obtain characterizations of the linear operators that strongly preserve the symmetric arctic ranks of symmetric matrices over nonnegative reals.

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Acknowledgement

Supported by : National Research Foundation of Korea

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