第1个回答 2018-11-27
因 a 为单位向量,则 a^Ta = 1. 由 A = aa^T, 则 A^2 = aa^Taa^T = a(a^Ta)a^T = aa^T = A,由 Ax = λx,左乘以A, A^2x = λAx = λ^2x A^2x - Ax = λ^2x - λx, (A^2-A)x = (λ^2-λ)x A^2 - A = O, λ^2-λ = 0, λ = 0, 1. 矩阵函数 f(A) 的特征值是 f(λ) 记单位向量 a = (a1, a2, ... , an)^T , 则 aa^T = [(a1)^2 a1a2 ... a1an] [a2a1 (a2)^2 ... a2an] [.................................] [ana1 ana2 ... (an)^2] 不是你写的那样。本回答被网友采纳