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Partial derivative of inverse of a matrix

zamzar
in Linear Algebra and Group Theory

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Hello,
I want to know if there is a formula to find the higher partial derivative of an inverse of a matrix with multi index.
You find the formula in attach fil.
I need this formula this weekend because I have a work to finich it and it rest for me just this one.
Thank you

post-114262-0-98752400-1445508833_thumb.jpg

Maybe not clever, but how I would start is by remembering that

 

[math]AA^{-1} = 1[/math]

 

and then use the chain rule to relate the derivatives of the inverse to the derivatives of the matrix. There maybe a clever way than this for the question you have asked.

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