#### 21.1.1 Creating Diagonal Matrices

The most common and easiest way to create a diagonal matrix is using the built-in function diag. The expression `diag (v)`, with v a vector, will create a square diagonal matrix with elements on the main diagonal given by the elements of v, and size equal to the length of v. `diag (v, m, n)` can be used to construct a rectangular diagonal matrix. The result of these expressions will be a special diagonal matrix object, rather than a general matrix object.

Diagonal matrix with unit elements can be created using eye. Some other built-in functions can also return diagonal matrices. Examples include balance or inv.

Example:

      diag (1:4)
    ⇒
    Diagonal Matrix

       1   0   0   0
       0   2   0   0
       0   0   3   0
       0   0   0   4

      diag (1:3,5,3)

    ⇒
    Diagonal Matrix

       1   0   0
       0   2   0
       0   0   3
       0   0   0
       0   0   0