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Thread: Find a transformation matrix [T] to get a specific matrix form.

  1. #1
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    Smile Find a transformation matrix [T] to get a specific matrix form.

    Hi geniuses.
    I desperately need urgent help, and I will be very grateful if someone could help me.

    My problem is how to find a transformation matrix [T] of a matrix [M], as specified in the example below:
    Let
    [M]=
    [a, b+jc, d+je;
    -b-jc, f, b+jc;
    -d-je, -b-jc, a ]

    As we notice that [M] is symetric

    Now let define
    N=
    [d+je, 0, 0;
    0, a, b+jc;
    0, -b-jc, f ]

    where the subMatrix
    [S]=
    [a, b+jc;
    -b-jc, f ].

    where [ T ]*[M]*[ T ]conjTr =[N]

    [S] has a special form as in this exemple is symetric , but could be hermitian, anti symetric, centrosymetric........etc



    The purpose, is to get the form of N. Without losing information. And the sub matrix [S] has a special form "detectable" like hermitian, symmetric, or per symmetric......
    Thank you,
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  2. #2
    MHF Contributor

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    Re: Find a transformation matrix [T] to get a specific matrix form.

    Frankly, I have no idea what you are doing here. Your very first assertion, that matrix [M] is symmetric, is clearly wrong. [M] is the sum of a diagonal and an anti symmetric matrix.
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  3. #3
    Newbie
    Joined
    May 2017
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    UK
    Posts
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    Re: Find a transformation matrix [T] to get a specific matrix form.

    I admit I lost focus when I wrote. yes [M] is an anti symmetric matrix.

    The Problem is

    How to find a transformation matrix [T] of a matrix [M], as specified in the example below:
    Let
    [M]=
    [a, b+jc, d+je;
    -b-jc, f, b+jc;
    -d-je, -b-jc, a ]

    As we notice that [M] is Anti-symetric

    Now let define
    N=
    [d+je, 0, 0;
    0, a, b+jc;
    0, -b-jc, f ]

    where the subMatrix
    [S]=
    [a, b+jc;
    -b-jc, f ].

    where [ T ]*[M]*[ T ]conjTr =[N]

    [S] has a special form as in this exemple is anti-symetric , but could be hermitian, anti symetric, centrosymetric........etc



    The purpose, is to get the form of N. Without losing information. And the sub matrix [S] has a special form "detectable" like hermitian, symmetric, or per symmetric......
    Thank you,
    Follow Math Help Forum on Facebook and Google+

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