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I don't understand how it is true. In my book there is a lemma which says:

Characteristic polynomial , determinant and Trace of a linear transformation of finite dimensional vector space are independent of chosen basis.

I understand that similar matrices have same characteristics polynomial,determinant and Trace but i don't understand how is it independent of chosen basis?

Luai Ghunim
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  • Actually writing out the argument for the trace with explicit bases is quite a nice exercise. After this, you can use that a change of basis is always $M \mapsto X M X^{-1}$ for some invertible matrix $X$, and use properties of the trace and the determinant. – Joppy Dec 11 '17 at 00:15
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    Two square matrices are similar if and only if they are the matrices of the same linear transformation with respect to different bases, as shown here. – David Dec 11 '17 at 00:18
  • @Luai Ghunim If you are ok, you can set as solved. Thanks! – user Dec 13 '17 at 07:33

1 Answers1

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The change of basis is a similarity transformation.

Take also a look here for more details:

Change of basis = similarity?

user
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