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Why similar matrices have the same characteristic polynomial? - Linear Algebra

Hi all,

Question: Explain both conceptually and algebraically why similar matrices have the same characteristic polynomial.

I have the proof for this but I'm not really sure how to explain why. Any ideas?

Thanks
Well, the proof is the algebraic explanation (I assume - I haven't seen the proof).

Conceptually: If A and B are similar, then for suitable choices of basis, they represent the same transformation. So if P(A)=0 you'd expect P(B) = 0 also.
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Oakenari
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Original post by DFranklin
Well, the proof is the algebraic explanation (I assume - I haven't seen the proof).

Conceptually: If A and B are similar, then for suitable choices of basis, they represent the same transformation. So if P(A)=0 you'd expect P(B) = 0 also.

Ah okay. I also assumed the proof was the algebraic explanation. Thank you very much.

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