Question

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.

Answer 1

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