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How can I make the most abbreviated expression of the resulting matrix?

Posted 11 years ago
Hi, I am trying to produce the most abbreviated expression of the formulas inside the resulting matrix
of the following code:
as = Variance[Table[u[i, t] - u[i, t - 1], {t, 1, 3}, {i, 1, 2}]];
MatrixForm[Simplify[as, Element[u[_, _], Reals]]];

cv = Covariance[Table[u[i, t] - u[i, t - 1], {t, 1, 3}, {i, 1, 2}]];
MatrixForm[Simplify[cv, Element[u[_, _], Reals]]];

MatrixForm[
D[Simplify[((as + 2*cv)^(1/2))*F, Element[u[_, _], Reals]], u[1, 2]]]

--> I am trying to abbreviate the result into the most simplfied expression of the resulting matrix only except the diagonal elements.

If so, how can I do this work?

Besides, when I try the different partial derivative formula like:
MatrixForm[
D[Simplify[((as + 2*cv)^(1/2))*F, Element[u[_, _], Reals]], u[1, 1]]]

The result of the position (1,1) of the resulting matrix is:
6^(1/2)* F *Abs'*[u[1, 0] - 2 u[1, 1] + u[1, 2]]

How can I fix this " Abs' " into the real number format that I can use practically?
 
I would greatly appreciate if I could get any helps on this problem.

Thank you very much!
POSTED BY: Woo Young Kang
Please see this post on the community about what Abs' is, why it written this way, and how to work with it:

http://community.wolfram.com/groups/-/m/t/158882

POSTED BY: Sean Clarke
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