How can I say that this occurs to each matrix individually and not to all of them together?

Question

I am translating a mathematical paper into English and I'm having trouble with this passage. What I wrote was:

"Comparing Equation A and Equation B, for example, for n=12 we note that the coefficient of X in Equation A tells us that there exist 15 matrices whose sum of its entries is 12 and whose respective weights can be 1 or -1..."

Specifically, my trouble is: I want to say that for each matrix the sum of the entries is 12 and not that the sum of the entries of all matrices is 12. Can it be inferred from what I wrote? If not, what would be a better way to write this? Also, I'm trying to modify the structure of the text in the original language as little as possible.

Thanks.

Answer 1

"There exist 15 matrices whose respective sums of entries are 12." This is more grammatically correct (since you are talking about 15 sums, not 1.) This makes it clear that you are talking about the set of sums, not the aggregate sum. Maybe some other contributes can help even more. The word "respective" specifies the one-to-one relationship between the sums and the matrices.

Answer 2

There exist 15 matrices, each having the sum of its elements equal to 12 and each having weights of either 1 or -1...

Answer 3

There is one word that is very useful - respective. Which you are already using.

Examples of usage

• The people present were John, Mara, Jake and Julie. They drove red, blue, blue and green cars, respectively, here.
• There 15 houses in the neighbourhood, which respectively use about 100 gallons of water daily.
• For the three front-runners in the mayoral election, Hassan, Hammoud and Hamid, their respective total campaign expenditures are $300K, $25K, and $5.
• I wish to assure you that for each issue listed here, we have their respective effective solution.

Therefore,

Comparing Equation A and Equation B, for example, for n=12 we note that the coefficient of X in Equation A tells us that there exist 15 matrices whose respective sum of entries is 12 and whose respective weight can be 1 or -1..."

respective (rɪˈspɛktɪv)

adj

1. belonging or relating separately to each of several people or things; several: we took our respective ways home.

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