gives the normalized form of a vector v.

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