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Linear maps preserving rank 2 on the space of alternate matrices and their applications

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  • Chongguang Cao
  • Xiaomin Tang

Abstract

Denote by 𝒦 n ( F ) the linear space of all n × n alternate matrices over a field F . We first characterize all linear bijective maps on 𝒦 n ( F ) ( n ≥ 4 ) preserving rank 2 when F is any field, and thereby the characterization of all linear bijective maps on 𝒦 n ( F ) preserving the max-rank is done when F is any field except for { 0 , 1 } . Furthermore, the linear preservers of the determinant (resp., adjoint) on 𝒦 n ( F ) are also characterized by reducing them to the linear preservers of the max-rank when n is even and F is any field except for { 0 , 1 } . This paper can be viewed as a supplement version of several related results.

Suggested Citation

  • Chongguang Cao & Xiaomin Tang, 2004. "Linear maps preserving rank 2 on the space of alternate matrices and their applications," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:808190
    DOI: 10.1155/S0161171204401161
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