Results And Applications Of Several Questions About The Quaternion Matrix

Through the research on the history and actuality of the quaternion and the quaternion matrix theory ,we have found that ,from 1843,when English mathematician W.R.Hamilton discovered the quaternion ,to the middle period of last century,the application of the quaternion and the quaternion matrix are discovered widely in geostatics,the theory of ped-top using, strap-down inertial ,naviation, enginery and organ,robot technology and artificial satellite attitude control,and so on. So it becomes a hotspot to study them in recent twenty years.By comparing the matrix theory over number field,we mainly discussed the quaternion matrix norm theory,the quaternionic determinant,the complex number expression of the quaternion matrix and the quarternion linear matrix equation. Concerning about the problem of the quaternion matrix analysis, we give in this paper the application of the quaternion matrix norm on the perturbation analysis of eigenvalue based on the definition of the quaternion matrix norm;and for the quaternion linear matrix equation,we give the structures and characters of the solution of the quaternion linear matrix equation AX-XB= 0,in which A,B∈SC_n(Q),and AX = XA,in which A∈SC_n(Q).