Proving Diagonalizability: A and B Are Similar and Diagonalizable

[cragar]

Homework Statement

show that if A is diagonalizable and if B is similar to A , then B is diagonalizable .

Suppose that (S^-1)AS=D and (W^-1)AW=B

S^-1 = S inverse

The Attempt at a Solution

so i solved for A and then plugged it in
getting
(S^-1)WB(W^-1)S=D

so we want to get it into the form ((SW)^-1)B(SW)=D
but i don’t know how to get there from the one above

 

[gabbagabbahey]

so we want to get it into the form ((SW)^-1)B(SW)=D

Not necessarily, you only need it to be in the form P^-1BP=D for some P...what do you get if you let P=W^-1S?

 

[cragar]

oh ok , i see , thanks for your help.