Results 1 to 3 of 3

Math Help - orthogonal matrices

  1. #1
    Member Jskid's Avatar
    Joined
    Jul 2010
    Posts
    160

    orthogonal matrices

    Show that if A and B are orthogonal matrices, then AB is an orthogonal matrix.

    I think I need to show that the columns of A are orthonormal to each other, but I don't know how.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Jskid View Post
    Show that if A and B are orthogonal matrices, then AB is an orthogonal matrix.

    I think I need to show that the columns of A are orthonormal to each other, but I don't know how.
    You often pick the hardest characterization to use. Try picking another one--solution below--use at your own risk

    Spoiler:


    You sure you want to look so soon?

    Spoiler:

    Fine, do it

    Spoiler:

    Isn't it true that A is real orthogonal if and only if A^{-1}=A^\top? So that (AB)^{-1}=B^{-1}A^{-1}=B^\top A^\top=(AB)^\top?


    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    A "tiny" alternative:

    M\in\mathbb{R}^{n\times n} is orthogonal iff MM^{t}=I

    So, (AB)(AB)^t=\ldots =I
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orthogonal Matrices
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 16th 2011, 05:28 PM
  2. Replies: 1
    Last Post: August 15th 2011, 04:32 AM
  3. orthogonal matrices help
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 9th 2011, 02:16 PM
  4. Orthogonal matrices
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 9th 2010, 10:00 PM
  5. Orthogonal matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 7th 2010, 04:21 AM

Search Tags


/mathhelpforum @mathhelpforum