摘要
Let Q be the quaternion division algebra over real field F.Denote by H_n(Q)the set of all n×n hermitian matrices over Q.We characterize the additive maps from H_n(Q) into H_m(Q)that preserve rank-1 matrices when the rank of the image of I_n is equal to n. Let Q_R be the quaternion division algebra over the field of real number R.The additive maps from H_n(Q_R) into H_m(Q_R)that preserve rank-1 matrices are also given.
Let Q be the quaternion division algebra over real field F, Denote by Hn(Q) the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn(Q) into Hm(Q) that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn (QR) into Hm (QR) that preserve rank-1 matrices are also given.
基金
Supported by NSF of China(10571033)
关键词
四元除法代数
加性映射
厄密共轭矩阵
秩
additive map
quaternion division algebra
Hermitian matrix
rank