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I read "f is a scalar function of a vector argument.". This means that the function f take one argument, and more specifically a vector (e.g. [1; 2.156; 1/3]), as input, and outputs a scalar, i.e. a simple real number (e.g. 1.159). E.g. f([1; 2.156; 1/3]) = 1.159.

I feel "of a vector argument" sounds weird. Is that correct, and if not what's the best way to phrase it?

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"f is a function of [some argument]" is completely correct terminology, specific to mathematics. From Columbia University's page "What does "function of" mean?":

A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on.

Here, "f is a function of a vector argument," is the mathematically appropriate phrase to express that the function f is defined by an argument that is a vector.

As noted below in the comments, you can leave off "argument" since the "...function of..." construction assumes that the object of "of" is an argument.

Finally, this is a construction particular to the discipline of mathematics, so don't expect native English speakers to be generally familiar with it. (Most people I know understand it perfectly, but most people I know are computer programmers!)

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  • Thanks! It sounds strange to my French ear, but I guess I'll get used to it :) – Franck Dernoncourt Sep 17 '14 at 14:50
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    @FranckDernoncourt It might sound a bit strange to many native English speakers, too, if they haven't studied mathematics :) – apsillers Sep 17 '14 at 14:52
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    @FranckDernoncourt If there's a weird bit here...I'd say it's only the lengthy "f is a function of a vector argument"...as opposed to "f is a function of a vector". When you start backing away from the convenience of mathematics contractions, you would expect other things to start expanding as well... such as to "f is a function that takes a vector argument". You either buy into the efficiency or you don't. – HostileFork says dont trust SE Sep 17 '14 at 14:53
  • In physics, a common name for scalar functions that depend on a vector is "scalar field". Maybe you prefer it over the much longer expression? – painfulenglish Sep 17 '14 at 15:31
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    For what it's worth: As a computer geek (albeit one who does not use Life gliders as his avatar -- yes, I saw what you did there), I think most of my friends would understand the phrase "[something] function of a [something] argument" just fine, though "scalar" and "vector" might not be recognized terms. – Jay Sep 17 '14 at 17:44

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