| Hermitian矩阵几何与保秩1的加法满射 |
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| 引用本文： | 黄礼平,李德琼,邓康. Hermitian矩阵几何与保秩1的加法满射[J]. 黑龙江大学自然科学学报, 2004, 21(4): 28-30 |
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| 作者姓名： | 黄礼平 李德琼 邓康 |
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| 作者单位： | 长沙理工大学,数学与计算科学学院,湖南,长沙,410076;长沙理工大学,数学与计算科学学院,湖南,长沙,410076;长沙理工大学,数学与计算科学学院,湖南,长沙,410076 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (10271021) |
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| 摘 要： | 设D是有对合的除环,介绍D上Hermitian矩阵几何研究的新结果,证明如果ψ是从D上n(n≥2)阶Hermitian矩阵空间到自身的保秩1的加法满射,则ψ是保粘切的双射.从而由Hermitian矩阵几何基本定理立刻得到ψ的公式.
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| 关 键 词： | 矩阵几何 Hermitian矩阵 有对合的除环 粘切性 |
Geometry of Hermitian matrices and additive rank-1-preserving surjective maps |
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| HUANG Li-ping,LI De-qiong,DENG Kang. Geometry of Hermitian matrices and additive rank-1-preserving surjective maps[J]. Journal of Natural Science of Heilongjiang University, 2004, 21(4): 28-30 |
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| Authors: | HUANG Li-ping LI De-qiong DENG Kang |
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| Abstract: | Let D be a division ring with an involution. New results on the geometry of Hermitian matrices over D is introduced. If ψ is an additive rank-1-preserving surjective map on Hn(D)(n ≥ 2), then ψ is a bijective map such that ψ preserves the adjacency. Thus, by the fundamental theorem of geometry of Hermitian matrices, the formula of ψ is obtained immediately. |
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| Keywords: | geometry of matrices Hermitian matrices division ring with an involution adjacency |
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