Let A and B be square matrices of same order. Prove that characteristic polynomials of AB and BA are same. Do AB and BA have same minimal polynomial ?

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Let A and B be square matrices of same order. Prove that characteristic polynomials of AB and BA are same. Do AB and BA have same minimal polynomial ?
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John D'Errico
John D'Errico 2020 年 7 月 30 日
This is not a question about MATLAB. Please don't post your homework assignments to Answers.

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回答 (1 件)

KSSV
KSSV 2020 年 7 月 30 日
Calculate the eigenvalues of the product. They will be euqal.
A = rand(2) ;
B = rand(2) ;
AB = eig(A*B)
BA = eig(B*A)

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