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3.7.2 Getting and Setting Pieces of Matrices

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]=

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]=