有关P_B~⊥P_A、P_A~⊥P_B的矩阵等式和秩等式

Matrix Equations and Rank Matrix Equations Related to P_B~⊥P_A and P_A~⊥P_B

在M=(A B)中,令A1=P⊥BPA,B1=P⊥APB,利用投影算子理论和矩阵秩方法可以得到关于A1,B1的一些矩阵等式和秩等式.

Let M =(A B),and assume that A1=P⊥BPA,B1=P⊥APB,.In this paper,the theory of projection and matrix rank methods are used to get a lot of matrix equations and matrix rank equations about A1,B1.