Let A and B be similar matrices. Prove that the geometric multiplicities of the eigenvalues of A and B are the same.(adsbygoogle = window.adsbygoogle || []).push({});

Some help I have gotten so far but still don't know how to proceed from there:

To prove that the geometric multiplicities of the eigenvalues of A and B are the same, we can show that, if B = P^-1 AP , then every eigenvector of B is of the form P^-1 v for some eigenvector v of A.

And i also know that for A and B to be similar matrices, these 5 properties must hold.

1. det A = det B

2. A and B have the same rank

3. A and B have the same characteristic polynomial

4. A and B have the same eigenvalues

5. A is invertible iff B is invertible

any help would be greatly appreciated

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# Homework Help: Linear Algebra : prove geometric multiplicities are the same

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