Linear Preservers of Doubly stochastic matrices and permutation matrices from $M_m$ to $M_n$
Volume 8, Issue 1, 2021, Pages 27-36
https://doi.org/10.22072/wala.2021.131790.1298
H. Baharlooei, M. Chaichi Raghimi, A. Bayati Eshkaftaki
Abstract Chi-Kwang Li, Bit-Shun Tam and Nam-Kiu Tsing have obtained necessary and sufficient condition for a linear operator on linear space of generalized doubly stochastic matrices to be strong preserver of doubly stochastic matrices and permutation matrices.
We show if a linear operator $T:M_m\rightarrow M_n$ is a (strong) preserver of doubly stochastic matrices, then $T$ is a (strong) preserver of the linear manifold of r-generalized doubly stochastic matrices and the linear space of generalized doubly stochastic matrices. Also we give necessary and sufficient condition for a linear operator $T:M_m\rightarrow M_n$ to be (strong) preserver of doubly stochastic matrices and permutation matrices.