http://i.imgur.com/F5KiXt1.jpg
想请问第三题该如何证明
想了很久都想不出如何利用rank=3的条件
麻烦各位大大帮忙解惑

det(A-λI)=0, since A is singular, det(A)=0, we haveλ=0 is a eigenvalue of A. dim{N(A-λI),λ=0} = dim{N(A)} = nullity = n-r = 4-3 = 1 = GM(λ=0)<=AM(λ=0). since A is 4x4, and λ≠0 has multiplicity 3 , so AM(λ=0) = 4-3 = 1.GM(λ=0)应该是1 你算错了 不过AM>=GM 要对角化每个λ一定要AM=GM(各eigenspace的基底总和=4) 题目没说清楚 不过从答案来看应该是指AM=GM的情况

所以这题的λ不为0的eigenvalue不用去验证am=gm囉？ 从题目好像没办法验证