Two-sided sgut-majorization and its linear preservers

Document Type : Research Paper

Author

Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box: 7713936417, Rafsanjan, Iran

Abstract

Let Mn,m be the set of all n-by-m real matrices, and let Rn be  the set of all n-by-1 real vectors. An n-by-m matrix R=[rij] is called g-row substochastic if ∑k=1mrik≤1  for all i (1≤i≤n).  For x, y∈Rn, it is said that x is sgut-majorized by y, and we write  x≺sguty  if there exists an n-by-n upper triangular g-row substochastic matrix R such that x=Ry. Define the relation ∼sgut as follows. x∼sguty if and only if x is   sgut-majorized  by y and y is sgut-majorized  by x.  This paper characterizes all (strong)  linear preservers   of  ∼sgut on Rn.

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References

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History

  • Receive Date: 15 June 2022
  • Revise Date: 17 September 2022
  • Accept Date: 25 November 2022

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