I want to define pure functions x(#1,#2) and y(#1,#2) like enter image description here But they aren't proper pure functions in the current form. How to modify the code?

  • 1
    $\begingroup$ You are missing an ampersand &. Example. $\endgroup$
    – Domen
    Commented Mar 12, 2023 at 10:28
  • $\begingroup$ thanks! In your example, how can one define x(#1,#2) and y(#1,#2) separately rather than x and y as a vector together? $\endgroup$
    – feynman
    Commented Mar 12, 2023 at 10:48

1 Answer 1


You have to reapply Function separately for x and y, for example:

{x, y} = Function @@@ (({{Cos[a], Sin[a]},{-Sin[a], Cos[a]}}) . ({{#1},{#2}}))

Example 1

If you want to have a "column vector" like notation on the left side, you have to properly match the levels, for example:

{{x}, {y}} = List@*Function @@@ ({{Cos[a], Sin[a]}, {-Sin[a], Cos[a]}} . {{#1}, {#2}});

{{x}, {y}} = Map[Function, {{Cos[a], Sin[a]}, {-Sin[a], Cos[a]}} . {{#1}, {#2}}, {2}];

Example 2

  • $\begingroup$ many thanks! I'm curious why for column vectors it's so much more work, as simply mimicking the row vector approach will yield an error saying: Lists {X} and Cos[a] #1+Sin[a] #2& are not the same shape. $\endgroup$
    – feynman
    Commented Mar 12, 2023 at 11:16

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