【摘要】 设S_m是复数域■上m×m对称矩阵全体。线性映射φ:S■_mS_n→S_mn保持矩阵张量积秩,即rankφ（A■B）=rank（A■B）,■A∈S_m,B∈S_n当且仅当存在可逆阵P∈M_mn使得φ（X）=PXP^t,■X∈S■_mS_n。本文是对矩阵张量积空间上的线性保持问题的补充和发展。更多还原

【Abstract】 Let S_m be the space of all m×m symmetric matrices over a complex field. A linear map φ:S■_mS_n→S_mn is said to be a rank preserver if rankφ（A■B）=rank（A■B）,■A∈S_m,B∈S_n. It is shown that φ:S■_mS_n→S_mn is a linear map preserving rank if and only if there exists an invertible matrix P∈M_mn such that φ（X）=PXP^t for every X∈S■_mS_n. This paper is a supplement and development of the linear preserving problem on the tensor product space of matrices.更多还原