Thread: Prove that similar matrices have the same characteristic equations

Hello,

I have been asked on an assignment to prove that similar matrices have the same characteristic equations. I believe that I would like to prove that . (L = lambda) The only idea I have had thus far is to take the inverse of the right hand side of that equation. The farthest I have reduced that to is , but even if that IS right, I don't know where to go from there. Any help would be great.

Sorry about the exponentialized -1s. I don't know how to properly display an exponent in the math code.

Thanks!

: [tex] x^{-1} [/tex]

: [tex] \lambda [/tex]

Originally Posted by nathron

Hello,

I have been asked on an assignment to prove that similar matrices have the same characteristic equations. I believe that I would like to prove that . (L = lambda) The only idea I have had thus far is to take the inverse of the right hand side of that equation. The farthest I have reduced that to is , but even if that IS right, I don't know where to go from there. Any help would be great.

Sorry about the exponentialized -1s. I don't know how to properly display an exponent in the math code.

Thanks!

Tonio

Ps. Of course, justify all the steps in the above proof.

Hey tonio,

Thanks for the reply. When you do the step , are you assuming that ?

Originally Posted by nathron

Hey tonio,

Thanks for the reply. When you do the step , are you assuming that ?

Yes, of course...and also the fact that scalar matrices commute with any matrix, so ...and use also left and right distributivity of matrix multiplicatio.

Tonio

Thanks!

You've been very helpful.