Linear Maps Preserving Inverses of Tensor Products of Hermite Matrices

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.