MATHEMATICA TUTORIAL

Getting and Setting Pieces of Matrices

m[[i,j]]the ^(th) entry
m[[i]]the i^(th) row
m[[All,i]]the i^(th) 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.
In[1]:=
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Out[1]=
This picks out the second row of the matrix.
In[2]:=
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Out[2]=
Here is the second column of the matrix.
In[3]:=
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This picks out a submatrix.
In[4]:=
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Out[4]=
m={{a11,a12,...},{a21,a22,...},...}assign m to be a matrix
m[[i,j]]=areset element to be a
m[[i]]=areset 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]]=areset 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.

Here is a 3×3 matrix.
In[5]:=
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Out[5]=
This resets the 2, 2 element to be , then shows the whole matrix.
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This resets all elements in the second column to be .
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This separately resets the three elements in the second column.
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This increments all the values in the second column.
In[9]:=
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A range of indices can be specified by using (Span).

This resets the first two rows to be new vectors.
In[10]:=
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This resets elements in the first and third columns of each row.
In[11]:=
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This resets elements in the first and third columns of rows 2 through 3.
In[12]:=
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Out[12]=
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