The only use of the word “matrix” I could find as a “military formation” is in the following example. Is this the usual word for a rectangular military formation? Is the word matrix used for more modern military formations, for example Napoleonic military formations? I look forward to your feedback.
ABSTRACT. In this article we undertake a study about the training process of the Roman soldier in the Epitoma rei militaris, document written during the last years of the fourth century a.D. We aim here to analyze the procedure reported by Vegetius view that aimed to to turn the recruit in soldier in the Roman army. We are supported in the concept of the Military Paideia, defining the process based on an ideal model of a soldier to problematize some essential points for the formation of the Roman soldier. We expect this work to develop an analysis of the elements of the Vegetius vision that they could form a Roman military matrix that would beat all the enemies.
I think that anyone who can compose “defining the process based on an ideal model of a soldier to problematize some essential points for the formation of the Roman soldier” will have no problem using words in any way they choose.
Agreed. IMO that’s pretentious academic gobbbledygook at its finest.
I’ve not heard “matrix” used as some special term of art in military parlance.
In modern non-military parlance the term “matrix” is sometimes used for a conglomerate of different ingredients forming a solid whole. e.g. “Concrete is a mixture of calcite and other microscopic mineral crystals with an embedded matrix of larger native rock.” (BS but plausible sentence I just made up.)
In that sentence the “matrix” is a semi-regular & semi-random 3D array of identifiable objects in the whole.
I could imagine by analogy somebody considering the individual soldiers to be like the stones in concrete. IOW, an essential part that, taken together with the binders of logistic support, doctrine, training, and leadership, add up to a solid and effective military “raw material” to build armies out of.
There’s more than academia-speak going on here. The paper linked to in the OP looks a bit like it may originally have been written in Portuguese, and then gone through a really clunky translation. Or at least like it was written by someone whose English skills are not stellar, to put it mildly.
As the for the OP’s question, the answer is “never”.
The “matrix” here means the combination of all the systems and standards of the Roman military: training, logistics, strategy, so on. The “Vegetius vision,” Rei militaris instituta, was literally a textbook for European commanders for centuries.