高师理科学刊
高師理科學刊
고사이과학간
JOURNAL OF SCIENCE OF TEACHERS＇ COLLEGE AND UNIVERSITY
2010年
6期
4-6
,共3页
实四元数%除环%保逆算子%自共轭矩阵
實四元數%除環%保逆算子%自共軛矩陣
실사원수%제배%보역산자%자공액구진
real quaternion%division ring%inverse preserver%self-conjugate matrix
设R,Q分别表示实数域、实四元数体.Mn(Q),SC(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(CCn(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.
設R,Q分彆錶示實數域、實四元數體.Mn(Q),SC(Q)分彆為Q上n×n全矩陣R-空間和n×n自共軛矩陣R-空間.設L為保逆算子且N-1(CCn(Q),Mn(Q))錶示從SCn(Q)到Mn(Q)所有保逆算子全體.研究瞭保逆算子L的性質,給齣瞭L的結構.
설R,Q분별표시실수역、실사원수체.Mn(Q),SC(Q)분별위Q상n×n전구진R-공간화n×n자공액구진R-공간.설L위보역산자차N-1(CCn(Q),Mn(Q))표시종SCn(Q)도Mn(Q)소유보역산자전체.연구료보역산자L적성질,급출료L적결구.
Suppose R and Q are the field of all real numbers and the real quaternion division ring respectively.Let Mn(Q) and SC(Q) be R-linear space of all n×n matrices and the set of all n×n self-conjugate matrices over Q respectively.Supposeis 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.
