How to prove the Eigenvalue property

Status
Not open for further replies.
C

claudiocamera

Full Member level 4
Joined
Aug 19, 2005
Messages
224
Helped
27
Reputation
54
Reaction score
6
Trophy points
1,298
Location
Salvador-BA-Brazil
Activity points
4,282
Hi there.

I was wondering how to prove the proposition below:

If S is nonsingular and B=SAS-1, then the eigenvalues of A and B coincides.

Any help ?
 

Re: Eigenvalue property

From the eigenvalue property:

Bx = λx, then we substitute B with SAS-1

SAS-1x = λx, we multiply both sides by S-1 on the left ( S is nonsingular so S-1 exist ) and we get

AS-1x = λS-1x, because λ is a number, so A has the same eigenvalue λ and the eigenvector is S-1x
 
Status
Not open for further replies.

Similar threads

Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…