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Question: Symbolic matrix calculus

Question:Symbolic matrix calculus

zohar 25 Maple
linear-algebra abstract
April 03 2019
2

How come maple doesn't support symbolic matrix calculus?

For example, I'd like to differentiate or simplify expressions with relation to general vectors and matrices. Besides simpifying the expressions, in runtime (e.g. optimizing a function in matlab) my vector and matrix size change according to the data, so deriving specific expressions element-wise would only be valid for a specific case.

A simple example (A is a matrix, x is a vector):

f(x) = ||Ax||^2

df/dx = 2A'Ax

Recently, I stumbled into this

http://www.matrixcalculus.org/

where you can try my example above: norm2(A*x)^2

I was wondering how come that mature symbolic softwares on the market (maple and mathematica) can't do it?
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