Simple question, fully expressed in the Title line. Is the dot within the parenthesis intended to mean, "any possible function"?

  • 2
    $\begingroup$ Just to avoid a dummy variable here. $\endgroup$
    – MonkeyKing
    May 17 '15 at 16:17
  • 3
    $\begingroup$ Unless $\cdot$ denotes a variable or a constant, I would believe $f(\cdot)$ means $f : x \mapsto f(x)$, although $f=f(\cdot$), so it's sort of pointless. $\endgroup$ May 17 '15 at 16:18
  • $\begingroup$ And how do you get the dot right in the middle with latex? $\endgroup$ May 17 '15 at 16:20
  • $\begingroup$ @toni Try \cdot $\endgroup$ May 17 '15 at 16:25
  • 7
    $\begingroup$ Just $f(\cdot)$ is rather pointless. The notation is more useful when you want to refer to a function which is defined in some more complicated fashion in terms of some other function. For instance $f=g(x,\cdot)$ is the same as $f(y)=g(x,y)$. Another important place is when you have a functional operator like convolution. For instance, $f(x,\cdot) * g(y,\cdot)$ means "convolve $f$ and $g$ in their second arguments, with the first arguments fixed as $x$ and $y$ respectively". It might be written as $f(x,z) *_z g(y,z)$. $\endgroup$
    – Ian
    May 17 '15 at 16:29

Usually we use it to avoid writing more letters $x$, $y$, etc. One example I see a lot: let $B: V \times V \to W$ be a bilinear form, and fix $y \in V$. When we write $B(\cdot, y)$, we mean the map $$V \ni x \mapsto B(x,y) \in W,$$ so we don't write this extra $x$ if we don't need to. If we're going to write $f(\cdot)$ just like this, as in the title question, then there isn't much advantage - just talk about the function $f$ and be done with it. The advantage I see is where you want to simplify the writing of some function that uses another one "in the background", like the example with the bilinear form I gave above.

  • 5
    $\begingroup$ When you write a function, you usually write $f:A \to B$, no? Instead of $A$ and $B$, I used $V$ and $W$. Also, $V \times V = \{ (x,y) \mid x,y \in V \}$ is the cartesian product that you have probably seen in some point of your life. And I used $B$ instead of $f$. So $B : V \times V \to W$ is a function $B$, from the set $V \times V$ to the set $W$. You can safely ignore the words "bilinear form" here - it was just for giving context to the explanation, but not needed at all. $\endgroup$
    – Ivo Terek
    May 17 '15 at 16:45
  • $\begingroup$ Does the "dot" have a name? $\endgroup$
    – Mel
    Jul 4 '17 at 3:37
  • $\begingroup$ Hmmm... "dot"? :-P $\endgroup$
    – Ivo Terek
    Jul 5 '17 at 15:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.