线性代数:设a为n×1阶矩阵,I为单位矩阵,A=I+aa^T,证明A为对陈矩阵.
问题描述:
线性代数:设a为n×1阶矩阵,I为单位矩阵,A=I+aa^T,证明A为对陈矩阵.
答
aa^T=(aa^T)^T
let a=(a1,a2,a3...an),the entry at i-th row and j-th colomn ofaa^T=ai*aj,the same time we have the entry that at j-th row and i-th is aj*ai,which is equal to ai*aj.
I=I^T
=>A=A^T