What is the correct phrasing for matrix Bellman nonhomogeneous equations?

[nomadreid]

TL;DR Summary

Is "the matrix Bellman nonhomogeneous equations" correct phrasing?

A paper that I am proof-reading contains this sentence.
"A universal method for solving the matrix Bellman nonhomogeneous equations was suggested in [82]."
This seemed a bit of an odd phrasing, so I asked the author to explain. He replied,
"I used the matrix Bellman nonhomogeneous equations, since these equations are matrix equations ."
Is this phrasing then correct? Or would "the Bellman nonhomogeneous matrix equations" be better? Or some third variant?

 

[.Scott]

There are "Bellman non-homogeneous equations" and there are "matrix equations".
But then there is the word "the"...
At best this is awkwardly worded.

There are two problems:

1) Fill me in on this: There are "Bellman differential equations". Are there non-homogeneous versions of them as well? Or has Bellman specifically considered a class of non-homogeneous equations which are referred to as the "Bellman non-homogeneous equations". If the "non-homogeneous" part is not something specifically addressed in Bellman's published works, then you would be working with "a non-homogeneous Bellman equation".

2) Then, given that "non-homogeneous" is part of the published work, we can ask the same thing about "matrix". What "the matrix Bellman non-homogeneous equations" implies is that published works by Bellman have been used in this paper to solve or otherwise work with matrices.

If that is what the author meant, I would say he is being correct but obscure. And it should be rephrased.
If that is not that he meant, then, at best, his statement is ambiguous to the point of being meaningless.

 

[nomadreid]

Thanks for the analysis, .Scott. Since this is not my field, I am not completely sure what the author meant; I asked him, and his answer was insufficient, so I will go with your "correct but obscure". I shall suggest that he rephrase it without suggesting a specific alternative, and let him deal with it, since I have no desire to find and pore over the corresponding references for his paper.

 

[.Scott]

I would pass on the entire analysis.
Without it, the author may not fully understand what the problem is.
In general, when someone has made an thoughtful but ambiguous statement, they are wholly unaware of the problem. It all makes perfect sense to them - and it seems to them that the rest of the world should have no problem with it at all.

Is this review a gate - or just a service to the author?

 

[nomadreid]

Thanks, .Scott. If I pass on your analysis, the author may ask the nature of the source. Shall I say that it is from a software engineer? The proof-reading is a paid service to the author. What is a gate in this context?

 

[.Scott]

A gate would be a review (or other activity) that must be passed before the document can be used for its main purpose. If there's one thing that SW engineers get to do more than code - it's review.

My analysis deals with the semantics. If you give the author the analysis, he can decide for himself whether he wants to change it. Since this is not a gate, it's entirely up to him how he uses your advice.

To be clear, the questions I posed were to the subject matter expert (the author), not you. And since this is not a gate, the only thing that you need to understand is my analysis - so you are prepared to explain it to the author. You can let the author decide whether he is being "correct and obscure" or "ambiguous to the point of meaningless". After all, he knows exactly what parts of what published materials he is referring to.