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Eigenvector math problem

  • #1

Homework Statement


Suppose that v is an eigenvector of both A and B with corresponding eigenvalues lambda and mui respectively. Show that v is an eigenvector of A+B and of AB and determine the corresponding eigenvalues


Homework Equations





The Attempt at a Solution


Av = lambda*v
Bv = mui*v
this is all i can think of....can someone give me a hint abt the next step?
 

Answers and Replies

  • #2
Pengwuino
Gold Member
4,989
15


Add the two equations together, tada! Of course, you'll need to exploit associativity... or linearity... man im always getting terms confused.
 
Last edited:
  • #3


u mean like:
(Av +Bv) = lambda*v + mui*v
(A+B)v = (lambda + mui) v
 
  • #4
Pengwuino
Gold Member
4,989
15


Yup! As for finding the eigenvalues of AB, simply multiply AB by v and remember that your eigenvalues are scalars that can move freely.
 

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