Results 1 to 7 of 7

Math Help - Similar matrices Q

  1. #1
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Similar matrices Q

    I'm a little rusty with my linear algebra, and was wondering how to prove that two matrices are similar. The question is:

    Two matrices A and B are said to be similar if there exists an invertible matrix S such that B = S^{-1}AS. Prove that A ~ A.

    So they want me to prove that A = S^{-1}AS, if I'm not mistaken. How do I show this? If I recall correctly, matrices are not commutative, so it's not a matter of cancelling out the S terms. Any guidance would be great!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: Similar matrices Q

    a=i^{-1}ai
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Re: Similar matrices Q

    So I always treat S as an identity matrix?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: Similar matrices Q

    Quote Originally Posted by Glitch View Post
    So I always treat S as an identity matrix?
    Not always; only in this case to show that A~A.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Re: Similar matrices Q

    Thanks. So say that I was proving A ~ B instead, how would the process differ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: Similar matrices Q

    Quote Originally Posted by Glitch View Post
    Thanks. So say that I was proving A ~ B instead, how would the process differ?
    The matrix S would depend on what A and B actually were. If A and B were different (yet similar!), we would get an S which was different from I.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Re: Similar matrices Q

    Ahh ok, thanks again.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Are these matrices similar?
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 24th 2011, 01:18 AM
  2. Another similar matrices Q
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: July 31st 2011, 02:47 AM
  3. similar matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 26th 2009, 05:26 PM
  4. Similar matrices
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 10th 2008, 06:17 PM
  5. Similar Matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 6th 2006, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum