Results 1 to 2 of 2

Thread: 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
    1,410
    Thanks
    1
    $\displaystyle (W-I)^T = 2W \ \ (\star)$

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

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

    Now take the transpose of both sides of $\displaystyle (\star)$ and solve for $\displaystyle I$. 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: Jul 17th 2011, 10:26 AM
  2. Symmetric relation v.s. symmetric matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Oct 14th 2010, 11:37 PM
  3. Replies: 3
    Last Post: Mar 18th 2010, 09:37 AM
  4. Prove Symmetric
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Oct 28th 2009, 06:33 AM
  5. Prove Matrices are symmetric
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Jan 28th 2009, 05:12 PM

Search Tags


/mathhelpforum @mathhelpforum