Results 1 to 2 of 2

Math Help - Prove that W is symmetric

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    48

    Prove that W is symmetric

    I know that:

    W = W transpose

    is symmetric,

    but how would I go about this question, how would I get started?

    Any help is appreciated!
    Attached Thumbnails Attached Thumbnails Prove that W is symmetric-capture3.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    (W-I)^T = 2W \ \ (\star)

    Using the property that: (A \pm B)^T = A^T \pm B^T

    we have that: W^T - I = 2W \ \Leftrightarrow \ {\color{blue}I = W^T - 2W}

    Now take the transpose of both sides of (\star) and solve for I. Compare this expression with what we have in blue and you should get what you want.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A is symmetric matrix and over R. A^10 = I. Prove A^2 = I
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: July 17th 2011, 10:26 AM
  2. Symmetric relation v.s. symmetric matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 14th 2010, 11:37 PM
  3. Replies: 3
    Last Post: March 18th 2010, 09:37 AM
  4. Prove Symmetric
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 28th 2009, 06:33 AM
  5. Prove Matrices are symmetric
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 28th 2009, 05:12 PM

Search Tags


/mathhelpforum @mathhelpforum