Linear Preservers of Doubly stochastic matrices and permutation matrices from $M_m$ to $M_n$

Document Type : Research Paper

Authors

1 Instietute of Advanced Studies, Payame Noor University, P.O. Box 19395- 3697, Tehran, Iran.

2 Department of Mathematic, Payame Noor University, P.O. Box 19395- 3697, Tehran, Iran.

3 Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, 88186-34141, Iran.

10.22072/wala.2021.131790.1298

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.

Keywords

References

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[3] C.K. Li, B.S. Tam and N.K. Tsing, Linear maps preserving permutation and stochastic matrices, Linear Algebra Appl., 341 (2002), 5-22.
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[6] M. Murray, Some Notes on Differential Geometry, University of Adelaide July 20, 2009.
Wavelet and Linear Algebra
Volume 8, Issue 1
Spring- Summer
2021
Pages 27-36

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