Map

Instead of using listability you can use Map to apply a function to every element in a matrix.

In[1]:=

Map will apply the function fun to every element in the matrix.

In[2]:=

Out[2]=

You can see the matrix that the sparse array represents. Note that because the function f did not have any definition, it is just kept wrapped around every element.

In[3]:=

Out[3]//MatrixForm=

Here, a function that squares its argument and divides the result by 5 is applied to every element in the matrix.

In[4]:=

Out[4]=

In[5]:=

Out[5]//MatrixForm=

When Map applies a function to a sparse array, it only operates on the elements that are actually stored (including the default element).

More information on Mathematica programming can be found in The Mathematica Book.