Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

Let $A$ be an $m \times n$ matrix. Let $a_{ij}$ be an element of $A$. What does the notation $\frac{\partial A}{\partial a_{ij}}$ mean?

share|improve this question
1  
In the absence of any clarification in the context, I'd say it was a complicated way to write $e_{ij}$, the matrix with $1$ at position $i,j$ and $0$ everywhere else. – Henning Makholm Oct 9 '12 at 19:26
Suppose I have the matrix A = [x y; y x]. Would $\frac{\partial A}{\partial a_{11}}$ = [1 0; 0 1]? This seems like it is what wikipedia is saying, but paper I am reading says otherwise. It says $\frac{\partial A}{\partial a_{11}}$ = [1 0; 0 0] – Stuart Oct 9 '12 at 19:26
@user19192: In that case I don't think $\frac{\partial A}{\partial a_{11}}$ has any clear meaning, since $a_{11}$ is not an independent variable that goes into the definition of $A$. Do you have more context of where you have seen this? – Henning Makholm Oct 9 '12 at 19:29
Ok, I understand. A is just a function of its m*n inputs. Not a concrete matrix. – Stuart Oct 9 '12 at 19:30
show 1 more comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.