## 3.7.2 Getting and Setting Pieces of Matrices

 m[[i, j]] the entry m[[i]] the row m[[All, i]] the column Take[m, {, }, {, }] the submatrix with rows through and columns through m[[{, ... , }, {, ... , }]] the submatrix with elements having row indices and column indices Tr[m, List] elements on the diagonal ArrayRules[m] positions of non-zero 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 matrix.
 In[1]:=  t = Array[a, {3, 3}]
 Out[1]=
This picks out the second row of the matrix.
 In[2]:=  t[[2]]
 Out[2]=
Here is the second column of the matrix.
 In[3]:=  t[[All, 2]]
 Out[3]=
This picks out a submatrix.
 In[4]:=  Take[t, {1, 2}, {2, 3}]
 Out[4]=

 m = {{, , ... }, {, , ... }, ... } assign m to be a matrix m[[i, j]] = v reset element {i, j} to be v m[[i]] = v reset all elements in row i to be v m[[i]] = {, , ... } reset elements in row i to be {, , ... } m[[All, j]] = v reset all elements in column j to be v m[[All, j]] = {, , ... } reset elements in column j to be {, , ... }

Resetting parts of matrices.
Here is a matrix.
 In[5]:=  m = {{a, b}, {c, d}}
 Out[5]=
This resets the 2, 2 element to be x, then shows the whole matrix.
 In[6]:=  m[[2, 2]] = x; m
 Out[6]=
This resets all elements in the second column to be z.
 In[7]:=  m[[All, 2]] = z; m
 Out[7]=
This separately resets the two elements in the second column.
 In[8]:=  m[[All, 2]] = {i, j}; m
 Out[8]=
This increments all the values in the second column.
 In[9]:=  m[[All, 2]]++; m
 Out[9]=

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