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Math Help - Derivatives of Matrices

  1. #1
    Junior Member
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    Derivatives of Matrices

    Hi everybody,

    I have attached the problem I encountered. --> Estimation of a parameter theta trough minimizing the sum of squares.
    How to get the derivative of this matrices and solve for theta?

    Thank you very much for any help or references.
    Attached Thumbnails Attached Thumbnails Derivatives of Matrices-minimize-sum-squares.jpg  
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  2. #2
    MHF Contributor

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    Re: Derivatives of Matrices

    Use the product rule treating the matrices as constants:
    \left[\left(X- A\theta\right)^t\left(X- A\theta\right)\right]'= (-A)^t(X- A\theta)- (X- A\theta)^t\A
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  3. #3
    Junior Member
    Joined
    Nov 2011
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    Re: Derivatives of Matrices

    Thank you very much!

    Now, I got the end result which I attached below!

    But how to get there from the derivative above?

    (I would also be happy about any online resources on how to manipulate such Matrix operations...)

    Here's the end result:
    Attached Thumbnails Attached Thumbnails Derivatives of Matrices-result-ls-method.jpg  
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