Strong preservers of symmetric arctic rank of nonnegative real matrices

A rank 1 matrix has a factorization as uvt 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 © 2019 Korean Mathematical Society. © 2019 Korean Mathematical Society.