This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


gives the normalized form of a vector v.
gives the normalized form of a complex number z.
normalizes with respect to the norm function f.
  • Normalize[v] is effectively v/Norm[v], except that zero vectors are returned unchanged.
  • Except in the case of zero vectors, Normalize[v] returns the unit vector in the direction of v.
  • Normalize is effectively , except when there are zeros in .
Symbolic vectors:
Use an arbitrary norm function:
is a complex-valued vector:
Normalize using exact arithmetic:
Use machine arithmetic:
Use 24-digit precision arithmetic:
Normalize a sparse vector:
Normalize a matrix by explicitly specifying a norm function:
Normalize a polynomial with respect to integration over the interval to :
is a symmetric matrix with distinct eigenvalues:
Power method to find the eigenvector associated with the largest eigenvalue:
This is consistent (up to sign) with what Eigenvectors gives:
The eigenvalue can be found with Norm:
is a random vector:
is the normalization of :
is a unit vector in the direction of :
New in 6