Problem:
Let D:= diag(λ1,…,λn), i.e., D is a diagonal matrix in Cn×n with entries λ1,…,λn ∈ C on its diagonal.
Find σ(D) and all eigenvectors of D.
My thoughts:
As the spectrum of D is the set of all eigenvalues, then σ(D) should be just λ1⋯λn = λnn .
But how can I find the eigenvectors ? I know I have to calculate the D - λI.
Can someone help me?
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