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Derivative of a matrix representation of a quadratic form


Is there any function X (perhaps in a Mathematica add-on) that would do
the following:

X[Dot[Dot[A,x],x],x] ---> Dot[A+Transpose[A],x]

X[Dot[Dot[A,x],a],x] ---> Dot[Transpose[A],a]

It seems to me that as such this is impossible, as vectors and matrices
are all the same to Dot. A realization of X would require something more
than Dot, perhaps several functions for various combinations of matrices
and vectors.

Has anybody already done this? Or does anybody know of a different package
that would help in manipulating long matrix expressions?

Please reply by email,
Thank you!

Nathan Cheng




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