радиус-вектор vs. вектор-строка

Question

Yesterday I came across the term радиус-вектор in physics, which surprised me because the order of the two parts is reversed by comparison with the terms вектор-строка and вектор-столбец in linear algebra, which I knew earlier. Does anyone have a suggestion for why it would be reasonable to use вектор as the second part of the term in one case but as the first part of the term in the other cases? For comparison, in English the terms are all built in the same way: radius vector, row vector, and column vector.

I don't know when these terms entered the language, but for instance if вектор-строка had been in use first then I'd think вектор-радиус would be a closer fit to the "established" format than радиус-вектор, and likewise for строка-вектор if радиус-вектор had been introduced first.

Answer 1

In compound nouns like

• самолёт-истреби́тель
• самолёт-разве́дчик
• самолёт-невиди́мка
• ве́ктор-строка́
• ве́ктор-столбе́ц
• спортсме́н-лы́жник
• спортсме́н-плове́ц
• садово́д-люби́тель

the first noun gives a more general description of the word and the second one gives a more specific description. First let's consider several other examples and then we'll discuss the words вектор-строка, вектор-столбец, and радиус-вектор. “Самолёт-невидимка” is an aircraft (this is a more general description) and more specifically, it's a stealth aircraft (this is a more specific description); it wouldn't make much sense to describe it as a stealth object (“невидимка”), which is more specifically a stealth aircraft. Similarly, “садовод-любитель” is a gardener — more specifically, an amateur gardener; again, it wouldn't make much sense to say that a “садовод-любитель” is an amateur, more specifically, an amateur gardener.

Similarly, “вектор-строка” is a vector — specifically a vector written as a row; “вектор-столбец” is a vector written as a column. It would make much less sense to say that “вектор-строка” is a row that forms a vector (there is no separate mathematical notion of row).

Now “радиус-вектор” is the position (radius) of a point, which is written as a vector. The word вектор specifies that радиус-вектор doesn't just give the distance to the position but also the direction.

Perhaps one could argue that “радиус-вектор” should be called “вектор-радиус” because it's a vector that (more specifically) gives the position of an object. I think the main reason “радиус-вектор” is used is the following: the term “радиус-вектор” is mostly used in physics, not in linear algebra. The word вектор just specifies the type of the variable: \vec r is “радиус-вектор”, whereas r is радиус (скаляр/scalar). If “радиус-вектор” was a concept studied in linear algebra and we had different kinds of vectors, then we would have terms like: вектор-радиус, вектор-ускорение, вектор-функция.

Summary To check what word order to use, you can apply the following test. Write A-B if you can say “он/она — A, а точнее A-B”:

Это самолёт, а точнее самолёт-истребитель. not Это истребитель, а точнее самолёт-истребитель.

Пусть v — произвольный вектор, а точнее вектор-столбец. not Пусть v — произвольный столбец, а точнее вектор-столбец.

Пусть \vec r — радиус (положение) частицы, а точнее её радиус-вектор. not Пусть \vec r — вектор частицы, а точнее её радиус-вектор.

Answer 2

An answer from a native speaker with a (somewhat rusty) math degree and no linguistic education.

If you're referring to this радиус-вектор, then the phrase emphasizes that this is a vector of some kind. "Vector" is the more important word here.

In linear algebra terminology, it's the difference between вектор-строка and вектор-столбец that's important. The differentiating word comes last, pushing "вектор" to the front.

This is more of a heuristic than a rule cast in stone.

Answer 3

Just as Vitaly Osipov said, the last word should be considered the main one, while the first is subordinate. So your question can be reformulated: why is ра́диус-ве́ктор more vector than radius, but ве́ктор-строка́ and ве́ктор-столбе́ц are more row / column than vector?

The answer, I think, is quite simple; it lies in common visual representation. This is definitely a column to me:

This is definitely a row:

And this is a vector:

Answer 4

Радиус-вектор is a vector, which is a radius, while for the single-row / single-column matrix, it's the other way around. The primary concept is that of a row or a column, and being a vector is secondary.

Besides, I would assume that радиус-вектор is an old compound, which was directly copied from, say, German: http://de.wikipedia.org/wiki/Ortsvektor . This is true of so many scientific terms! English wasn't an influential language of science (and in general) in Russia until the 20th century. That's why so many words familiar to the English speaker look strange or have a queer stress in Russian.

"Вектор-строка" and "вектор-столбец" look to my eye like native-coined terms. We didn't use them at all, mostly just referring to rows and columns as "строка" as "столбец". In German, they're Spaltenvektor and Zeilenvektor, so the words were definitely not borrowed as is.