湖南科技大学学报（自然科学版）
湖南科技大學學報（自然科學版）
호남과기대학학보（자연과학판）
JOURNAL OF HUNAN UNIVERSITY OF SCIENCE & TECHNOLOGY（NATURAL SCIENCE EDITION）
2014年
4期
125-128
,共4页
正交(P,Q)对称解%正交投影%正交三角分解%通解
正交(P,Q)對稱解%正交投影%正交三角分解%通解
정교(P,Q)대칭해%정교투영%정교삼각분해%통해
orthogonal (P,Q)-symmetric solution%orthogonal triangular decomposition%orthogonal invariance%general expression
定义了正交（P，Q ）－对称矩阵的概念，通过矩阵的正交投影构造了它的结构，针对正交（P，Q ）－对称矩阵的正交不变性，采用直接代入法把问题转化为求矩阵方程组的正交解，利用矩阵的正交三角分解得出了矩阵方程组有正交（P，Q ）－对称解的充分必要条件，及通解的表达式。最后得出矩阵方程AX＝B有正交（P，Q ）－对称解的充要条件及通解表达式。
定義瞭正交（P，Q ）－對稱矩陣的概唸，通過矩陣的正交投影構造瞭它的結構，針對正交（P，Q ）－對稱矩陣的正交不變性，採用直接代入法把問題轉化為求矩陣方程組的正交解，利用矩陣的正交三角分解得齣瞭矩陣方程組有正交（P，Q ）－對稱解的充分必要條件，及通解的錶達式。最後得齣矩陣方程AX＝B有正交（P，Q ）－對稱解的充要條件及通解錶達式。
정의료정교（P，Q ）－대칭구진적개념，통과구진적정교투영구조료타적결구，침대정교（P，Q ）－대칭구진적정교불변성，채용직접대입법파문제전화위구구진방정조적정교해，이용구진적정교삼각분해득출료구진방정조유정교（P，Q ）－대칭해적충분필요조건，급통해적표체식。최후득출구진방정AX＝B유정교（P，Q ）－대칭해적충요조건급통해표체식。
Puts forward the concept of orthogonal (P,Q )-symmetric matrix,and the structure was constructed through the orthogonal projection.According to the orthogonal invariance of orthogonal (P,Q)-symmetric matrix,The problem was converted to solve orthogonal solutions of matrix equations by adopting direct substitution method.Applying the orthogonal triangular decomposition for matrix ,necessary and sufficient conditions were derived and the general expression was gotten for the orthogonal solution to the matrix equations. The necessary and sufficient conditions were derived and the general expression was put forward for the orthogonal (P,Q)-symmetric solution to the matrix equation AX=B.
