gives the two-dimensional unit vector in the k direction.
gives the n-dimensional unit vector in the k direction.
Details and Options
- UnitVector[n,k] 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.
Examplesopen allclose all
Basic Examples (2)
The unit vector in the direction in two dimensions:
The unit vector in the direction in three dimensions:
A unit vector in dimension 100:
A machine‐precision unit vector in the direction in two dimensions:
A 50‐digit-precision unit vector in the direction in two 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:
Properties & Relations (1)
A random unit vector:
The length is equal to n:
There is a 1 in position k:
All other components are zero:
Possible Issues (1)
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:
Introduced in 2007
Updated in 2008