Here is my attempt to explain the difference between conjunctions @: and @

   ]A =: 2 3 $ 1 2 3 4 5 6
1 2 3
4 5 6
   |. A  NB. Reverse matrix A
4 5 6
1 2 3
   |."1 A  NB.  Reverse each row of A (each 1-cell)
3 2 1
6 5 4
   |. @: (|."1) A  NB.  Reverse the result of |."1 A
6 5 4
3 2 1
   |. @ (|."1) A  NB. Reverse each reversed row of A
1 2 3
4 5 6

In general, f @: (g"r) y means apply f to the result of g"r y and f @ (g"r) y 
means apply f separately to the results of applying g to each r-cell of y.  
When r is not specified, the right rank of g is used.

You may be able to guess from this what happens when f @: g and f @ g are used 
dyadically!

Kip Murray

Sent from my iPad

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