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}]
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| This picks out the second row of the matrix. | |
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| Here is the second column of the matrix. | |
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| This picks out a submatrix. | |
In[4]:=
Take[t, {1, 2}, {2, 3}]
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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}}
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| This resets the 2, 2 element to be x, then shows the whole matrix. | |
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| This resets all elements in the second column to be z. | |
In[7]:=
m[[All, 2]] = z; m
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| This separately resets the two elements in the second column. | |
In[8]:=
m[[All, 2]] = {i, j}; m
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| This increments all the values in the second column. | |
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