Mathematica HowTo
How to | Get Parts of a Matrix
Mathematica has many matrix operations that support operations such as building, computing, and visualizing matrices. It also has a rich language for picking out and extracting parts of matrices.
Define the following matrix. Note how a matrix in Mathematica is not restricted to number entries:
 Out[1]//MatrixForm=
Use Part to go to the first row and take the second element:
 Out[2]=
Or use the shorthand notation [[...]] for Part:
 Out[3]=
To take an entire row, use one index to specify the row:
 Out[4]=
To take an entire column, you need to select all rows with All and specify the column:
 Out[5]=

To pick out a submatrix you can use Span (;;). First define a 4×5 matrix:
 Out[6]//MatrixForm=
The top-left 3×4 matrix with bold entries here corresponds to rows 1 through 3 and columns 1 through 4:
 Out[7]//MatrixForm=
Extract the highlighted matrix by using the short form ;; of Span to specify the relevant span of rows and columns:
 Out[8]=
 Out[9]//MatrixForm=
Extract all elements except the outermost rows and columns (negative indices count from the end):
 Out[10]=
 Out[11]//MatrixForm=