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 allclose allBasic Examples (1)Summary of the most common use cases

https://wolfram.com/xid/0binefxg-wwmef

Scope (5)Survey of the scope of standard use cases

https://wolfram.com/xid/0binefxg-lvafnn

Use an arbitrary norm function:

https://wolfram.com/xid/0binefxg-iwgj6a


https://wolfram.com/xid/0binefxg-yvefc
Normalize using exact arithmetic:

https://wolfram.com/xid/0binefxg-l8ce20


https://wolfram.com/xid/0binefxg-di4n8p

Use 24‐digit precision arithmetic:

https://wolfram.com/xid/0binefxg-o499d5


https://wolfram.com/xid/0binefxg-cz3qh2


https://wolfram.com/xid/0binefxg-c28yhw


https://wolfram.com/xid/0binefxg-b8uret

Normalize a TimeSeries:

https://wolfram.com/xid/0binefxg-397g5y

https://wolfram.com/xid/0binefxg-8gd40a


https://wolfram.com/xid/0binefxg-1hdxcf


https://wolfram.com/xid/0binefxg-yawamn


https://wolfram.com/xid/0binefxg-bfacom


https://wolfram.com/xid/0binefxg-6b5bfc

Generalizations & Extensions (2)Generalized and extended use cases
Applications (1)Sample problems that can be solved with this function
m is a symmetric matrix with distinct eigenvalues:

https://wolfram.com/xid/0binefxg-xdjek

Power method to find the eigenvector associated with the largest eigenvalue:

https://wolfram.com/xid/0binefxg-1b3ud

This is consistent (up to sign) with what Eigenvectors gives:

https://wolfram.com/xid/0binefxg-h4js08

The eigenvalue can be found with Norm:

https://wolfram.com/xid/0binefxg-hqvb10

Properties & Relations (1)Properties of the function, and connections to other functions
Wolfram Research (2007), Normalize, Wolfram Language function, https://reference.wolfram.com/language/ref/Normalize.html.
Text
Wolfram Research (2007), Normalize, Wolfram Language function, https://reference.wolfram.com/language/ref/Normalize.html.
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.
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
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: 19-June-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: 19-June-2025
]}