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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]=

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=

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]=

Constructing special types of matrices with SparseArray.

This sets up a general lower-triangular matrix.

In[8]:= SparseArray[{i_, j_}/;i>=j -> f[i, j], {3, 3}] // MatrixForm

Out[8]//MatrixForm=