A list has a Head at its zero index position
lst = {1, 2, 3}; Head[lst] Out[242]= List lst[[0]] Out[243]= List
By changing the head we use Apply. For example, to add the numbers of the above lst, we need to change the Head from List to Plus. There is a command in Mathematica to change the Head, called Apply
Plus @@ lst Out[244]= 6
We could have used the zero index trick, but it is better to use Apply:
lst[[0]] = Plus Out[245]= Plus lst Out[246]= 6
If we have a list of lists, like this
lst = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} Out[247]= {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}
And we wanted to change the head of each list in it, for example, we want the product of each list shown, then we need to change the head of each list to Times. To do that, the follwing short but might be strange looking command
Apply[Times, lst, {1}] Out[248]= {6, 120, 504}
Another way to do the above is to Map the Apply function
(Times @@ #1 & ) /@ lst Out[249]= {6, 120, 504}
or, little shorter version of the above:
(Times @@ #1 & ) /@ lst Out[250]= {6, 120, 504}