With square matrix B=P^(-1) A P, prove det(tI-B)=det(tI-A)

[1234567k]

With square matrix B=P^-1AP, prove det(tI-B)=det(tI-A)
thanks!!!

I have one more question:
If a matrix P can be expressed as V^-1CV
must C be diagonal?

thanks!

 

[Deleted member 4993]

With square matrix B=P^-1AP, prove det(tI-B)=det(tI-A)
thanks!!!

I have one more question:
If a matrix P can be expressed as V^-1CV
must C be diagonal?

thanks!

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[1234567k]

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

Opps sorry, i saw the instruction after i post

My only step can do is prove that det(A) =det(B)
But I found that det(tI-A) ≠det(tI-B) if i only know det(A) =det(B)
So i think i went to a wrong direction

I was thinking in diagonalization, but no idea

Thank you!