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=

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