四元数体上矩阵方程AXA*=B的非负定解(英文)  

Nonnegative definite solution of the matrix equation AXA=B over quaternion field

作　　者：李桃生[1] 赵小妹[1] 孙志敏[1] 

机构地区：[1]华中师范大学数学系,武汉430079

出　　处：《华中师范大学学报（自然科学版）》2002年第4期403-408,共6页Journal of Central China Normal University：Natural Sciences

摘　　要：讨论了四元数体上矩阵方程AXA*=B的非负定解,解决了以下问题:(1)给出了四元数体上矩阵方程AXA*=B存在非负定解的充分必要条件;(2)当矩阵方程AXA*=B的非负定解存在时,给出了通解的表达式和解的加法分解式;(3)若X是矩阵方程AXA*=B的非负定解,给出了求X的秩的公式以及X为最小秩或最大秩解的条件.This paper studies the nonnegativedefinite solution of the matrix equation AXA*=B over quaternion field. The following problems are solved: (1) The necessary and sufficient condition for the existence of the nonnegativedefinite solution to the matrix equation AXA*=B; (2) If the equation AXA*=B is consistent, we give a representation of the general solution to AXA*=B and an additive decomposition of the solutions; (3) If X is an nonnegativedefinite solution to AXA*=B, we give the formula for the rank of X and the conditions under which X is a maximal or minimal rank solution.

关 键 词：矩阵方程 非负定解 四元数体 非负定矩阵 正定矩阵 满秩分解 1-逆 

分 类 号：O151.23[理学—数学] O241[理学—基础数学]