| 自共轭四元数矩阵空间的保行列式加法映射 |
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| 引用本文： | 李艳君,任秋萍,张权.自共轭四元数矩阵空间的保行列式加法映射[J].高师理科学刊,2009,29(5):31-33. |
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| 作者姓名： | 李艳君 任秋萍 张权 |
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| 作者单位： | 1. 齐齐哈尔大学,理学院,黑龙江,齐齐哈尔,161006
2. 黑龙江科技学院数力系,黑龙江,哈尔滨,150027 |
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| 摘 要： | 设Q是一个实四元数体,SCn(Q)是Q上n×n自共轭四元数矩阵空间,f是从SCn(Q)到自身的映射,如果对任意A,B∈SCn(Q),都有f(A+B)=f(A)+f(B),且det(f(A))=det(A),则称f是SCn(Q)上的保行列式加法映射.刻画了n≥3时SCn(Q)上的保行列式加法映射的形式.
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| 关 键 词： | 秩 保持问题 自共轭矩阵 行列式 四元数 |
Additive preservers of determinant on self-conjugate quaternion matrix spaces |
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| LI Yan-jun,REN Qiu-ping,ZHANG Quan.Additive preservers of determinant on self-conjugate quaternion matrix spaces[J].Journal of Science of Teachers＇College and University,2009,29(5):31-33. |
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| Authors: | LI Yan-jun REN Qiu-ping ZHANG Quan |
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| Institution: | LI Yan-jun1,REN Qiu-ping2,ZHANG Quan1(1.School of Science,Qiqihar University,Qiqihar 161006,China,2.Department of Mathematics and Mechanics,Heilongjiang Institute of Science and Technology,Harbin 150027,China) |
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| Abstract: | Let Q be a real quaternion division ring,SCn(Q)be the space of all n × nself-conjugate quaternion matrices overQ.If a map f :S C n(Q)→SCn(Q),satisfying f(A+B)=f(A)+f(B)and det(f(A))=det(A)for any A,B∈SCn(Q),then f is called a additive preserver of determinant on SCn(Q).Characterized the additive preservers of determinant on SCn(Q)(n≥3). |
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| Keywords: | rank preserving problem self-conjugate quaternion matrix determinant quaternion |
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