Linear Algebra .
Suppose P is invertible & A=PBP^-1. Solve for B in terms of A.

How do i go by solving this problem?

Question

Linear Algebra .
Suppose P is invertible & A=PBP^-1. Solve for B in terms of A.

How do i go by solving this problem?

amistre64 · Answer

use the inverses ....

amistre64 · Answer

since P P' = 1,  and  P' P = 1 ; do the proper left right multiplications of P and P'

anonymous · Answer

Yeah I is the identity matrix so do i have to do it to both sides of the equation?

amistre64 · Answer

one of the basic rules of algebra is ... whatever yo do to one side, do to _______ ?

anonymous · Answer

you do to the other. I wasn't sure because it said solve in terms of A

amistre64 · Answer

a = pbp'

p' a = p' pbp'

p' a = bp'

p' a p = bp' p

p' a p = b

amistre64 · Answer

now b is in terms of a, right?

anonymous · Answer

Yeah thanks, i didn't know you had to take the inverse of P again in order to cancel out the 1st P but thanks for the explanation

amistre64 · Answer

good luck ;)