行分块矩阵值域上正交投影的展开式

Expansion Formulas for Orthogonal Projectors onto Ranges of Row Block Matrices

中文关键词:  Moore-Penrose逆  正交投影  等式  不等式  秩公式.

英文关键词:Moore-Penrose inverse  orthogonal projector  equality  inequality  rank formula.

中文摘要:

      给出了分块矩阵$[A, B]$值域上正交投影的一些展开公式,并用这些展开公式刻画矩阵$A$, $B$和$[A, B]$值域上正交投影的关系.特别地给出了两个正交投影可交换的一些判别条件.

英文摘要:

      We give in this note some expansion formulas for the orthogonal projectors onto the range of the row block matrix $[\, A, \, B \,]$, and use the expansion formulas to examine relations among the orthogonal projectors onto the ranges of $A$, $B$ and $[\, A, \, B \,]$. In particular, we present some identifying conditions for a pair of orthogonal projectors of the same size to commute.