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Math Help - Converting A Function to Matrix...?

  1. #1
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    Converting A Function to Matrix...?

    Hey guys,

    Iv been given the function:

    V(x,y) = kx^2 + k[(y-x)^2] + ky^2

    They say :

    Write down a symetric matrix A such that V = (X^T)AX where X = (x,y)^T

    T: Transpose of matrix.

    Whaaaat the helll???

    Thanks.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by outspired View Post
    Hey guys,

    Iv been given the function:

    V(x,y) = kx^2 + k[(y-x)^2] + ky^2

    They say :

    Write down a symetric matrix A such that V = (X^T)AX where X = (x,y)^T

    T: Transpose of matrix.

    Whaaaat the helll???

    Thanks.
    The want you to find a 2\times2 symmetric matrix such that:

    \left[\begin{array}{cc}x&y\end{array}\right]\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=kx^2+k(y-x)^2+ky^2=2kx^2-2kxy+2ky^2

    Multiplying out that matrix product gives you ax^2+bxy+cxy+dy^2. So what do a,b,c,d need to be in order to make the equation hold? Remember that A has to be symmetric.
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  3. #3
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    Thanks man, i did something like that but it didnt come out like that. You just need to take the co-effients of the equation and match it with the equation determined by the multiplication....by the way, how did you know they were looking for a 2x2?

    a = 2k

    b+c = -2k => b=c=-k

    d = 2k
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  4. #4
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by outspired View Post
    Thanks man, i did something like that but it didnt come out like that. You just need to take the co-effients of the equation and match it with the equation determined by the multiplication....by the way, how did you know they were looking for a 2x2?

    a = 2k

    b+c = -2k => b=c=-k

    d = 2k
    Because of the rules governing matrix multiplication. We were multiplying

    [1\times2]\cdot[m\times n]\cdot[2\times1]

    To multiply the first two, m must be 2. To multiply the second pair, n must be 2.
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  5. #5
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    Wow...i never saw it that way.

    Thanks alot man...you've just given me 3 minutes of extra sleep...JOY.
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