BUILT-IN MATHEMATICA SYMBOL

UnitVector

UnitVector[k]
gives the two-dimensional unit vector in the k

direction.

gives the n-dimensional unit vector in the k

direction.

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]=

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:

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: