I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about simple matrix algebra, but not calculus.

I would specifically like to know if with the addition of Tensor package in version 9, if the following is possible:

$a, \lambda \in R^n$, and $C\in R^{n\times n}$ Here $n$ is unknown/symbolic variable.

I am trying to find derivative of expressions which involve matrix-vector products such as (to give a simple example) $f(a,\lambda)=\dfrac{\lambda^T Ca}{\sqrt{a^T C a}}$

I would like to know if using Mathematica we can find expressions of $\dfrac{\partial f}{\partial a}$ etc.


  • $\begingroup$ version 9? That's almost 2 years old now... did you mean 10? $\endgroup$ – rm -rf Jul 28 '14 at 17:45
  • $\begingroup$ I mention version 9 since it seems to me thats when the Tensor package was added. I don't know if 10 adds anything more to this functionality. $\endgroup$ – nonlinearism Jul 28 '14 at 17:48
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    $\begingroup$ AFAIK these things are not possible, not out of the box. See also mathematica.stackexchange.com/questions/52213/… $\endgroup$ – Teake Nutma Jul 28 '14 at 19:45
  • $\begingroup$ Thats disappointing, if true. $\endgroup$ – nonlinearism Jul 28 '14 at 21:15
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    $\begingroup$ A similar question was asked at mathematica.stackexchange.com/questions/3242/… regarding purely symbolic computations of vector derivatives of matrix/vector expressions of unspecified rank. AFAIK it's not straightforward to do, unfortunately. $\endgroup$ – DumpsterDoofus Jul 28 '14 at 23:53

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