摘要
设R记实数域,Q记R上四元数代数,若x∈EQ,x=a+bi+cj+dk,其中a、b、c、d在R中,则x的共轭元=a—bi—cj—dk,x的范数N(x)=a^2+b^2+c^2+d^2。设Q^(×n)(或R^(×))记Q(或R)上n×n矩阵构成的R代数,我们以Hom(Q~×,R^(4×4))记Q^(×)的全部R代数表示的集合。还以E_(ij)表示(i,j)位置是1,其余位置是0的n阶方阵,I_r记r阶单位阵;GLr(Q)及GLr(R)分别记Q上及R上一般线性群。
In this paper,we determind all the 4n-th-order real representa—tions of quaternion n-th-order square matrix algebra on real namber field, then, applied this result to determine whether the quternion matrix is or not irregular, meanwhile, obtained a new proof of quaternion matrix Hadarmand inequality.
