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Math Help - Orthogonal projection.

  1. #1
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    Orthogonal projection.

    Hi.

    I am quite clueless about the following problem and need help on where to start.

    given

    y =

    [1 2]
    [3 4]

    x1 =

    [1,0]
    [0,0]

    x2 =

    [1,0]
    [0,1]

    (these are all 2x2 matricies by the way, not vectors).

    Record the orthogonal decomposition of Y obtained by orthogonally projecting Y onto L(X1,X2).


    I have no idea where to start on this.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Orthogonal projection.

    How the inner product is defined?
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  3. #3
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    Re: Orthogonal projection.

    The inner product is defined as

    <AB> = tr(A'B)

    sorry for not including that.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: Orthogonal projection.

    Quote Originally Posted by Kuma View Post
    The inner product is defined as <AB> = tr(A'B)
    Hint Working in coordinates with respect to the canonical basis of \mathbb{R}^{2\times 2} the inner product is the usual one in \mathbb{R}^4 i.e. <(x_1,x_2,x_3,x_4),(y_1,y_2,y_3,y_4)>=x_1y_1+x_2y_  2+x_3y_3+x_4y_4 . Now, use any of the well known standard methods.
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