1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra: equivalence

  1. Apr 22, 2010 #1
    1. The problem statement, all variables and given/known data
    1) two linear transformations B and C are equivalent iff there exist invertible linear transformations P and Q such that PB=CQ
    2) if A and B are equivalent then so are A' and B' in dual space
    3) Do there exist linear transformations A and B such that A and B are equivalent but A^2 and B^2 are not?
    4) Does there exist a linear transformation A such that A is equivalent to a scalar a but A is not equal to a?

    3. The attempt at a solution
    I really don't know where to start. I know that if two l.ts. A and B are equivalent then (AB)^-1 = B^-1A^-1. But that's where I am now.
    Last edited: Apr 22, 2010
  2. jcsd
  3. Apr 22, 2010 #2
    Ok for the first question, two lts B and C are equivalent iff there exist lts E and F such that
    B = E^-1 C F
    Now let E = P and let F=Q, we have
    B= P^-1 C Q or PB = CQ so this means that the lts P and Q must be invertible?
  4. Apr 23, 2010 #3
    Can you please repeat your definition for equivalence between A and B? I'm not sure I follow.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Linear algebra: equivalence
  1. Linear Algebra (Replies: 5)

  2. Linear Algebra (Replies: 1)