四元数体上Hermitian矩阵空间保秩1的加法映射

数学季刊 ›› 2007, Vol. 22 ›› Issue (4): 482-491.

四元数体上Hermitian矩阵空间保秩1的加法映射

1.Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China; 2.Department of Mathematics, Harbin Institute of Technology, Harbin 150001,China

收稿日期:2006-09-18 出版日期:2007-12-30 发布日期:2023-10-18
作者简介: HAN Jing-wen(1980-), female, native of Hengshui, Hebei, an assistant of Tianjin University of Finance and Economics, engaged in classical groupe and matrix algebra; ZHENG Bao-dong(1960-), male, native of Harbin, Heilongjiang, a professor of Harbin Institute of Technology, engaged in classical groups and its application.
基金资助:
Supported by NSF of China(10571033)

Additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra

1.Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China; 2.Department of Mathematics, Harbin Institute of Technology, Harbin 150001,China

Received:2006-09-18 Online:2007-12-30 Published:2023-10-18
About author: HAN Jing-wen(1980-), female, native of Hengshui, Hebei, an assistant of Tianjin University of Finance and Economics, engaged in classical groupe and matrix algebra; ZHENG Bao-dong(1960-), male, native of Harbin, Heilongjiang, a professor of Harbin Institute of Technology, engaged in classical groups and its application.
Supported by:
Supported by NSF of China(10571033)

摘要/Abstract

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 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.

关键词: additive map, quaternion division algebra, Hermitian matrix, rank

Abstract: 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 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.

Key words: additive map, quaternion division algebra, Hermitian matrix, rank

中图分类号:

O151.2

韩敬稳, 郑宝东. 四元数体上Hermitian矩阵空间保秩1的加法映射[J]. 数学季刊, 2007, 22(4): 482-491.

HAN Jing-wen, ZHENG Bao-dong . Additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(4): 482-491.

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