This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# UnitVector

 UnitVector[k] gives the two-dimensional unit vector in the k direction. UnitVectorgives the n-dimensional unit vector in the k direction.
• UnitVector is a list of length n with a 1 in position k and 0s elsewhere.
• UnitVector by default creates a vector containing exact integers.
• The option WorkingPrecision can be used to specify the precision of vector components.
The unit vector in the direction in 2 dimensions:
The unit vector in the direction in 3 dimensions:
The unit vector in the direction in 2 dimensions:
 Out[1]=

The unit vector in the direction in 3 dimensions:
 Out[1]=
 Scope   (2)
A unit vector in dimension 100:
A machine-precision unit vector in the direction in 2 dimensions:
A 50-digit-precision unit vector in the direction in 2 dimensions:
 Applications   (3)
Find the matrix for a "black box" linear operator:
The matrix is equivalent to (though perhaps less efficient than) the "black box":
The matrix form allows you to use typical linear algebra functions:
p is a random permutation:
Get the permutation matrix:
Compute the unit matrices:
A random unit vector:
The length is equal to n:
There is a 1 in position k:
All other components are zero:
For very large dimensions, n, the vector given by UnitVector may use a lot of memory:
An alternative is to use a SparseArray to represent the same thing: