Results 1 to 4 of 4

Math Help - Need help in Matrix Decomposition

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    12

    Need help in Matrix Decomposition

    Hi all,

    I have the product of a 4x3 rectangular matrix and its transpose (the transpose is a 3x4 matrix). The product is a 4x4 symmetric matrix.

    How can I find the original 4x3 rectangular matrix, if I know the values of all the elements of the 4x4 product matrix?

    If anyone could help me solve this problem, i would realy appreciate it.
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by dimper129 View Post
    Hi all,

    I have the product of a 4x3 rectangular matrix and its transpose (the transpose is a 3x4 matrix). The product is a 4x4 symmetric matrix.

    How can I find the original 4x3 rectangular matrix, if I know the values of all the elements of the 4x4 product matrix?

    If anyone could help me solve this problem, i would realy appreciate it.
    Thanks

    The only matrix you have is the 4x4? Can you post this matrix and any others?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    12
    Quote Originally Posted by pickslides View Post
    The only matrix you have is the 4x4? Can you post this matrix and any others?
    Yes the only matrix I have is the 4x4 product.
    e.g. if

    \left[\begin{matrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \\ a_{10} & a_{11} & a_{12} \end{matrix}\right]\left[\begin{matrix}  a_1 & a_4 & a_7 & a_{10} \\ a_2 & a_5 & a_8 & a_{11} \\ a_3 & a_6 & a_9 & a_{12} \end{matrix}\right] = \left[\begin{matrix} 0.0018 & -0.0062 & -0.0009 & 0.0021 \\ -0.0062 & 0.0537 & -0.0027 & 0.0014 \\ -0.0009 & -0.0027 & 0.1142 & 0.0063 \\ 0.0021 & 0.0014 & 0.0063 & 0.1005 \end{matrix}\right]

    then how can I find the values of a_1, a_2 ... upto  a_{12}

    Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2009
    Posts
    12
    It makes 10 equations in 12 unkowns like

    {a_1}^2 + {a_2}^2 + {a_1}^2 = 0.0018
    a_1a_4 + a_2a_5 + a_3a_6 = -0.0062
    a_1a_7 + a_2a_8 + a_3a_9 = -0.0009
    a_1a_{10} + a_2a_{11} + a_3a_{12} = 0.0012
    {a_4}^2 + {a_5}^2 + {a_6}^2 = 0.0537
    a_4a_{7} + a_5a_{7} + a_6a_{9} = -0.0027
    a_4a_{10} + a_5a_{11} + a_8a_{12} = 0.0014
    {a_7}^2 + {a_8}^2 + {a_9}^2 = 0.1142
    a_7a_{10} + a_8a_{11} + a_8a_{12} = 0.0063
    {a_{10}}^2 + {a_{11}}^2 + {a_{12}}^2 = 0.1005

    we can solve (approximate) this non-linear system of equations in MATLAB using "fsolve" function. But this does not solve my problem because I need exact solution.

    Does anyone know how to do it?

    Thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. decomposition of r.v.
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 5th 2011, 03:48 PM
  2. QR Decomposition
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 11th 2010, 08:36 PM
  3. Spectral Decomposition of a Matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 17th 2010, 11:03 AM
  4. Jordan Decomposition to Schur Decomposition
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 30th 2009, 01:52 PM
  5. Proof: every Hermitian matrix has eigenvalue decomposition
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 16th 2009, 10:53 AM

Search Tags


/mathhelpforum @mathhelpforum