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Thread: Derivatives of Matrices

  1. January 12th 2012, 06:17 PM #1
    Marmy
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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. January 13th 2012, 03:59 AM #2
    HallsofIvy
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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. January 13th 2012, 07:03 AM #3
    Marmy
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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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