Proving similar matrices if diagonal have same entries which are eigenvalues

Math_Fortnite_Lover

New member
Joined
Oct 30, 2021
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3
I know that since (A-tI)x+0, the diagonal matrix has all the eigenvalues.

I also have proved in my homework that similar matrices have the same eigenvalues. But I am stuck on how to show that in a proof way. Any help would be appreciated?

Screenshot 2021-10-30 131522.png
 

blamocur

Full Member
Joined
Oct 30, 2021
Messages
580
I believe similar matrices have identical characteristic polynomials, which means that their sets of eigenvectors are identical too.
 
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