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xEnOnn
 3 years ago
How I show that the eigenvalues of matrix A times matrix B is and BA are equal? That's to show eigenvals(AB)=eigenvals(BA).
xEnOnn
 3 years ago
How I show that the eigenvalues of matrix A times matrix B is and BA are equal? That's to show eigenvals(AB)=eigenvals(BA).

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hahd
 3 years ago
Best ResponseYou've already chosen the best response.0http://en.wikipedia.org/wiki/Characteristic_polynomial think it might be useful

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.0From this, \[\det(AB\lambda I)=0\] Since AB and BA are different matrices, I still find it strange that their eigenvalues would turn out the same. How is this so?

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1Suppose \[ABx=\lambda x\] then multiply by B \[BABx=\lambda Bx\] so \[BA(Bx)=\lambda (Bx)\] thus BA has the same eigenvalues as AB similarly AB has the same eigenvalues as BA.

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.0wow...this is smart... thanks a lot Zarkon!! :D
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