Indexing an array in Mathematica

Questions
1

I would like to select out specific elements of an array (two dimensional) in order to operate on them. What is the proper syntax for indexing through an array in Mathematica (specifying both dimensions)?

2

The function is Part

http://reference.wolfram.com/language/ref/Part.html?q=Part

A small example:

In[3]:= anArray = {{1, 2, 3, 4}, {5, 6, 7, 8}}

Out[3]= {{1, 2, 3, 4}, {5, 6, 7, 8}}

In[5]:= anArray[[2, 3]]

Out[5]= 7

In[6]:= anArray[[2, 3]] = "Happy"

Out[6]= "Happy"

In[7]:= anArray

Out[7]= {{1, 2, 3, 4}, {5, 6, "Happy", 8}}
3

If you have a 2D array and want to slice out part to operate on, you can use the ;; notation in the array indices. For example, given a 3x4 array you can extract the 2x2 subarray for rows 2-3, columns 3-4 as follows.

In[1]:= a = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}

Out[1]= {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}

In[2]:= a[[2 ;; 3, 3 ;; 4]]

Out[2]= {{7, 8}, {11, 12}}

You can use the same notation to then modify that region of the array:

In[3]:= a[[2 ;; 3, 3 ;; 4]] = {{-1, -2}, {-3, -4}}

Out[3]= {{-1, -2}, {-3, -4}}

In[4]:= a

Out[4]= {{1, 2, 3, 4}, {5, 6, -1, -2}, {9, 10, -3, -4}}