- #1
gimpy
- 28
- 0
Ok well i have two questions.
1) If B = P^-1AP and let X be an eigenvector of A corresponding to the eigenvalue y. Show that y is an eigenvalue of B and find a corresponding eigenvector.
This is what i did.
AX=yI and since B = P^-1Ap -> A = PBP^-1
so (PBP^-1)X=yI
Now this is the part where i get lost. Am i on the right track?
2) If A and B are nxn matrices, A is invertable, show that BA is similar to AB.
So BA = P^-1ABP because BA is similar to AB. But I am kinda lost now. I'm sure i have to do something with the fact that A is invertable. Umm... A^-1...
1) If B = P^-1AP and let X be an eigenvector of A corresponding to the eigenvalue y. Show that y is an eigenvalue of B and find a corresponding eigenvector.
This is what i did.
AX=yI and since B = P^-1Ap -> A = PBP^-1
so (PBP^-1)X=yI
Now this is the part where i get lost. Am i on the right track?
2) If A and B are nxn matrices, A is invertable, show that BA is similar to AB.
So BA = P^-1ABP because BA is similar to AB. But I am kinda lost now. I'm sure i have to do something with the fact that A is invertable. Umm... A^-1...