## 3.7.1 Constructing Matrices

 Table[f, {i, m}, {j, n}] build an matrix where f is a function of i and j that gives the value of the entry Array[f, {m, n}] build an matrix whose entry is f[i, j] DiagonalMatrix[list] generate a diagonal matrix with the elements of list on the diagonal IdentityMatrix[n] generate an identity matrix Normal[SparseArray[{{, }->, {, }->, ... }, {m, n}]] make a matrix with non-zero values at positions {, }

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]=
This makes a matrix with two non-zero values filled in.
 In[5]:=  Normal[SparseArray[{{2, 3}->a, {3, 2}->b}, {3, 4}]]
 Out[5]=
MatrixForm prints the matrix in a two-dimensional form.
 In[6]:=  MatrixForm[%]
 Out[6]//MatrixForm=

 Table[0, {m}, {n}] a zero matrix Table[Random[ ], {m}, {n}] a matrix with random numerical entries Table[If[i j, 1, 0], {i, m}, {j, n}] a lower-triangular matrix

Constructing special types of matrices with Table.
Table evaluates Random[ ] separately for each element, to give a different pseudorandom number in each case.
 In[7]:=  Table[Random[ ], {2}, {2}]
 Out[7]=

 SparseArray[{}, {n, n}] a zero matrix SparseArray[{i_, i_} -> 1, {n, n}] an identity matrix SparseArray[{i_, j_}/;ij -> 1, {n, n}] a lower-triangular matrix

Constructing special types of matrices with SparseArray.
This sets up a general lower-triangular matrix.
 In[8]:=  SparseArray[{i_, j_}/;ij -> f[i, j], {3, 3}] // MatrixForm
 Out[8]//MatrixForm=

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