Monday, November 11, 2019

linear algebra - Eigenvalues and Eigenvectors of diagonal marix

Problem:




Let D:= diag(λ1,,λn), i.e., D is a diagonal matrix in Cn×n with entries λ1,,λnC 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 λ1λn = 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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