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.
- For a complex number z, Normalize[z] returns z/Abs[z], except that Normalize gives 0.
- Normalize[expr,f] is effectively expr/f[expr], except when there are zeros in f[expr].
Examplesopen allclose all
Basic Examples (1)
Use an arbitrary norm function:
Normalize using exact arithmetic:
Use 24‐digit precision arithmetic:
Normalize a TimeSeries:
Generalizations & Extensions (2)
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:
Wolfram Research (2007), Normalize, Wolfram Language function, 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.
Wolfram Language. (2007). Normalize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Normalize.html