• Support PF! Buy your school textbooks, materials and every day products Here!

Solving for B matrix in terms of A. Can someone check my answer?

  • Thread starter thepatient
  • Start date
  • #1
164
0

Homework Statement



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

Homework Equations



(AB)^-1 = B^-1*A^-1

The Attempt at a Solution



multiply from the left of each side of the equation by P^-1:
P^-1 *A = BP^-1

Take the inverse of both sides:

(P^-1*A)^-1 = (BP^-1)^-1
A^-1 * P = P*B^-1

Multiply from the left of each side of the equation by P^-1:
P^-1*A^-1*P = B^-1

Take the inverse of both sides:

[P^-1(A^-1*P)]^-1 = B

B = (A^-1*P)^-1*P
B = P^-1 *A * P


Is that correct?
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,508
730
Yes, it looks OK but is much more complicated than it needs to be. At the first step where you have ##P^{-1}A= BP^{-1}## just multiply by ##P## on the right.
 
  • #3
164
0
Hahaaaa. That's right. Thanks. :]
 
  • #4
164
0
I wasn't sure if you can multiply from the right too.
 
  • #5
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,705
1,722
I wasn't sure if you can multiply from the right too.
Why not? Two matrices can be multiplied as long as their row and column numbers match up properly. If all three of A, B and P (and P^(-1)) are nxn they can be multiplied in any order.

RGV
 

Related Threads for: Solving for B matrix in terms of A. Can someone check my answer?

Replies
1
Views
2K
Replies
1
Views
2K
Replies
5
Views
1K
Replies
2
Views
858
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
4
Views
2K
Replies
2
Views
604
Replies
4
Views
1K
Top