Getting and Setting Pieces of Matrices
| m[[i,j]] | the   entry |
| m[[i]] | the i row |
| m[[All,i]] | the i column |
| Take[m,{i0,i1},{j0,j1}] | the submatrix with rows  through  and columns  through  |
| m[[i0;;i1,j0;;j1]] | the submatrix with rows  through  and columns  through  |
| m[[{i1,...,ir}, {j1, ... , js}]] | the r×s submatrix with elements having row indices  and column indices  |
| Tr[m,List] | elements on the diagonal |
| ArrayRules[m] | positions of nonzero elements |
Ways to get pieces of matrices.
Matrices in Mathematica are represented as lists of lists. You can use all the standard Mathematica list-manipulation operations on matrices.
Here is a sample 3×3 matrix.
| Out[1]= |  |
This picks out the second row of the matrix.
| Out[2]= |  |
Here is the second column of the matrix.
| Out[3]= |  |
This picks out a submatrix.
| Out[4]= |  |
| m={{a11,a12,...},{a21,a22,...},...} | assign m to be a matrix |
| m[[i,j]]=a | reset element  to be a |
| m[[i]]=a | reset all elements in row i to be a |
| m[[i]]={a1,a2,...} | reset elements in row i to be  |
| m[[i0;;i1]]={v1,v2,...} | reset rows  through  to be vectors  |
| m[[All,j]]=a | reset all elements in column j to be a |
| m[[All,j]]={a1,a2,...} | reset elements in column j to be  |
| m[[i0;;i1,j0;;j1]]={{a11,a12,...},{a21,a22,...},...} | reset the submatrix with rows  through  and columns  through  to new values |
Resetting parts of matrices.
| Out[5]= |  |
This resets the 2, 2 element to be
, then shows the whole matrix.
| Out[6]= |  |
This resets all elements in the second column to be
.
| Out[7]= |  |
This separately resets the three elements in the second column.
| Out[8]= |  |
This increments all the values in the second column.
| Out[9]= |  |
A range of indices can be specified by using 
(Span).
This resets the first two rows to be new vectors.
| Out[10]= |  |
This resets elements in the first and third columns of each row.
| Out[11]= |  |
This resets elements in the first and third columns of rows 2 through 3.
| Out[12]= |  |
