0
$\begingroup$

a biologist/ecologist here,

I never took any courses in algebra (definitely missing in my education) but I am working with matrices all day.

For one paper, I have to write the matrix formulation but I am unsure of the conventions and how to write this:

  |1|2|3|4| j
1| 0 0 0 1
2| 0 0 0 0
3| 0 1 1 1
4| 0 1 0 0
i

Let's assume this binary matrix of i rows and j columns (Aij), I want to compute the sum of rows and columns i and j where i = j. A column and a row contains info on one species (i=1 and j=1 contains info on species i). I call my ensemble of species k.

For each species k, I want to calculate the sum of a species abundance (wk) multiplied by the sum of 1 in a species row and column (so sum of aik and akj). For instance, when k=1, the sum would be (0+0+0+0)+(0+0+0+1) = 1

So far I wrote this:

https://i.stack.imgur.com/aJp7u.png

Is this correct? Is there a better/simpler notation?


\begin{equation*} wG=\frac{\sum ^{S}_{k=1} \ \left( w_{k} \ \sum ^{S}_{i=1}( a_{ik} +a_{ki}) \ \right)}{\sum ^{S}_{k=1} w_{k}} \ where\ i=j \end{equation*}

$\endgroup$
0
$\begingroup$

If you want to add the entries of the $k$th row with the entries of the $k$th column, then the sum would be $$ \sum_{i=1}^n \left( a_{ik} + a_{ki} \right). $$

$\endgroup$
  • $\begingroup$ And I guess precise that i=j. Thanks! $\endgroup$ – Pierre O Mar 20 '19 at 8:21
  • $\begingroup$ \begin{equation*} wG=\frac{\sum ^{S}_{k=1} \ \left( w_{k} \ \sum ^{S}_{i=1}( a_{ik} +a_{ki}) \ \right)}{\sum ^{S}_{k=1} w_{k}} \ where\ i=j \end{equation*} $\endgroup$ – Pierre O Mar 20 '19 at 16:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.