摘要
设R,Q分别表示实数域、实四元数体.Mn(Q),SCn(Q)分别为Q上n×n全矩阵R-空间和n×n自共轭矩阵R-空间.设L为保逆算子且N-1(SCn(Q),Mn(Q))表示从SCn(Q)到Mn(Q)所有保逆算子全体.研究了保逆算子L的性质,给出了L的结构.
SupposeR andQare the field of all real numbers and the real quaternion division ring respectively.Let M n（Q） and SCn（Q） be R-linear space of all n × n matrices and the set of all n × n self-conjugate matrices over Q respectively.Suppose L is an inverse preserver and N-1（SCn（Q）,Mn（Q））denotes the set of inverse preservers from SCn（Q） to Mn（Q）.Researched the characterization of above L,gave the forms of of L.
出处
《高师理科学刊》
2010年第6期4-6,共3页
Journal of Science of Teachers＇College and University
基金
Nation science foundation of China(10671026)
关键词
实四元数
除环
保逆算子
自共轭矩阵
real quaternion
division ring
inverse preserver
self-conjugate matrix
