摘要
设U和V是有限维Hilbert空间X的2个子空间,P_U和P_V分别表示从X到U和V上的正交投影矩阵.在一定的条件下,给出了P_U和P_V在空间分解X=U⊕U⊥下的分块矩阵表示.利用此结果和矩阵分块的技巧,研究了2个正交投影矩阵可以交换的充要条件.
Let U and V be subspaces of a finite dimensional Hilbert space X,P_U and P_V be orthogonal projection matrices of Xonto U and V,respectively.Under certain condition,the blocked matrices of PU and P_V on the space decomposition X=U ⊕U⊥were presented respectively.Using this and the technique of matrix block,the necessary and sufficient conditions under which PU and PV are commutative were studied.
出处
《上海应用技术学院学报（自然科学版）》
2015年第4期393-396,415,共5页
Journal of Shanghai Institute of Technology: Natural Science
基金
上海市高校青年教师培养基金资助项目(ZZyyy12021)
上海应用技术学院引进人才基金资助项目(YJ2012-21)
关键词
正交投影矩阵
分块矩阵
交换矩阵
orthogonal projection matrix
blocked matrix
commutative matrices
