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Normalize

Normalize[v]
gives the normalized form of a vector v.

Normalize[z]
gives the normalized form of a complex number z.

Normalize[expr, f]
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[0] gives 0.

Normalize[expr, f] is effectively expr/f[expr], except when there are zeros in f[expr].

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 matrix by explicitly specifying a norm function:

Normalize a polynomial with respect to integration over the interval -1 to 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:

v is a random vector:

u is the normalization of v:

u is a unit vector in the direction of v: