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3.7.1 Constructing Matrices


Functions for constructing matrices.










  • This generates a matrix whose


    entry is a[


    i,j].
  • In[1]:= Table[a[i, j], {i, 2}, {j, 2}]

    Out[1]=

  • Here is another way to produce the same matrix.
  • In[2]:= Array[a, {2, 2}]

    Out[2]=

  • DiagonalMatrix makes a matrix with zeros everywhere except on the leading diagonal.
  • In[3]:= DiagonalMatrix[{a, b, c}]

    Out[3]=




  • IdentityMatrix[n] produces an


    identity matrix.
  • In[4]:= IdentityMatrix[3]

    Out[4]=

    Of the functions for constructing matrices mentioned above, Table is the most general. You can use Table to produce many kinds of matrices.


    Some special types of matrices.

  • Table evaluates Random[] separately for each element, to give a different pseudorandom number in each case.
  • In[5]:= Table[Random[ ], {2}, {2}]

    Out[5]=

  • This gives a tridiagonal matrix.
  • In[6]:= Table[Switch[i-j, -1, a, 0, b, 1, c, _, 0],
    {i, 5}, {j, 5}]

    Out[6]=

  • MatrixForm prints the matrix in a two-dimensional array, and makes the structure in this case clearer.
  • In[7]:= MatrixForm[%]

    Out[7]//MatrixForm=