Normalize
Details
- 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.
- For a complex number z, Normalize [z] returns z/Abs [z], except that Normalize [0] gives 0.
- Normalize [expr,f] is effectively expr/f[expr], except when there are zeros in f[expr].
Examples
open all close allBasic Examples (1)
Scope (5)
Symbolic vectors:
Use an arbitrary norm function:
v is a complex‐valued vector:
Normalize using exact arithmetic:
Use machine arithmetic:
Use 24‐digit precision arithmetic:
Normalize a sparse vector:
Normalize a TimeSeries :
Generalizations & Extensions (2)
Normalize a matrix by explicitly specifying a norm function:
Normalize a polynomial with respect to integration over the interval to :
Applications (1)
m 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 :
Properties & Relations (1)
v is a random vector:
u is the normalization of v:
u is a unit vector in the direction of v:
Tech Notes
History
Text
Wolfram Research (2007), Normalize, Wolfram Language function, https://reference.wolfram.com/language/ref/Normalize.html.
CMS
Wolfram Language. 2007. "Normalize." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Normalize.html.
APA
Wolfram Language. (2007). Normalize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Normalize.html
BibTeX
@misc{reference.wolfram_2025_normalize, author="Wolfram Research", title="{Normalize}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/Normalize.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_normalize, organization={Wolfram Research}, title={Normalize}, year={2007}, url={https://reference.wolfram.com/language/ref/Normalize.html}, note=[Accessed: 17-November-2025]}