两种局部算子的性质

Properties of Two Local Operators

给定矩阵A,若矩阵P满足PA=A,则称P为局部恒等算子,若满足P2A=PA,则称P是局部幂等的。给出两类局部算子的一些性质:P局部恒等当且仅当P-I=U(I-AA-);P局部幂等的当且仅当P2-P=U(I-AA-),以及他们之间的关系。局部恒等算子显然是局部幂等。

For a given matrix A, a matrix P such that PA = A is said to be a local identity, and such that P2A = PA is said to be a local idempotent. Some properties of such operators are presented： P is local identity if and only if P - I = U（ I - AA^ - ）, P is local idempotent if and only if p2 -p = U（I - AA ^- ）. Moreover, their relation is also demonstrated： local identity clearly is local idempotent.