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Linear Maps Preserving Inverses of Tensor Products of Hermite Matrices

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  • Shuang Yan
  • Yang Zhang

Abstract

Let C be a complex field, H_{m_1m_2} be a linear space of tensor products of Hermite matrices H_{m_1}⊗H_{m_2} over C , and suppose m_{1}, m_2≥2 are positive integers. A linear map f -H_{m_1m_2} → H_n is called a linear inverse preserver if f( X_{1} ⊗X_{2} )^{-1}= f( X_{1}⊗X_{2}) ^{-1} ) for arbitrary invertible matrix X_{1} ⊗ X_{2}∈ H_{m_{1}m_{2}} .The aim of this paper is to characterize the linear maps preserving inverses of tensor products of Hermite matrices.

Suggested Citation

  • Shuang Yan & Yang Zhang, 2024. "Linear Maps Preserving Inverses of Tensor Products of Hermite Matrices," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 15(4), pages 1-75, December.
    • Handle: RePEc:ibn:jmrjnl:v:15:y:2024:i:4:p:75
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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