Results 1 to 4 of 4

Math Help - matrix

  1. #1
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    matrix

    Nice to see the forum back again. It has been down for weeks hasn't it?

    A question says: "Cayley proved in 1946 that, if S is a skew-symmetric matrix, then I+S is non-singular and A=(I-S)(I+S)^-1 is orthogonal. Find A when S=(0 3, -3 0) and show that it is orthogonal."

    The second row of S is -3 0. I don't know why I am not able to find A. I will probably manage the final part myself.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Re: matrix

    $\begin{bamtrix}1 & 0\\
    0 & 1
    \end{batrix}-
    \begin{bmatrix}
    0 & 3\\
    -3 & 0
    \end{bmatrix} =
    \begin{bmatrix}
    1 & -3
    3 & 1
    \end{bmatrix}$

    So then what is I + S?

    Let B=I+S. Then the inverse of B is
    $\frac{1}{\text{det}(B)}\begin{matrix}
    b_{22} & -b_{21}\\
    -b_{12} & b_{11}
    \end{bmatrix}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2012
    From
    Ohio
    Posts
    3

    Re: matrix

    Is The Matrix,
    | 0 3 |
    | -3 0 |
    And,
    | 1 -3|
    | 3 1 |

    IF these are the two matrices please tell everyone, Please also Define I & S
    A series of good videa tutorials on matrices can be found !

    Sorry, didnt realise there was a post above the one shown on my screen. I see the question now i am just gonna leave my post as it is for now though. sorry.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    Re: matrix

    The first matrix you give is S. I had been making a mistake by multiplying by the determinant instead of dividing. The expression is straightforward to evaluate. The last part is done using the property AxAtranspose=I.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 27th 2010, 03:07 PM
  2. [SOLVED] Elementary matrix, restore to identity matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 13th 2010, 09:04 AM
  3. unitary and upper triangular matrix => diagonal matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 10th 2009, 06:52 PM
  4. Replies: 3
    Last Post: March 17th 2009, 10:10 AM
  5. finding check matrix from generating matrix
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: June 3rd 2008, 04:27 AM

Search Tags


/mathhelpforum @mathhelpforum