# 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)
• Accepted : 2019.02.07
• Published : 2019.11.01
• 113 12

#### 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.

#### Acknowledgement

Supported by : National Research Foundation of Korea

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