# Unitary transformation

by Amith2006
Tags: transformation, unitary
 P: 421 Can it be said that similarity transformation is a transformation in real space while unitary transformation is a transformation in complex space?
 P: 1,705 lol what? an orthonormal transformation is a similarity transformation in real space. a unitary transformation is a similarity transformation in complex space. they're really the same thing, it's just that a unitary transformation is one that preserves lengths of complex numbers, which can be viewed as vectors on an argand diagram, while an orthonormal transformation preserves lengths of real vectors.
P: 421
 Quote by ice109 they're really the same thing, it's just that a unitary transformation is one that preserves lengths of complex numbers, which can be viewed as vectors on an argand diagram, while an orthonormal transformation preserves lengths of real vectors.
Since a unitary transformation preserves lengths and angle between the complex numbers in the 2 basis, doesn't it make sense to say its operates in a complex space?

P: 1,705
Unitary transformation

 Quote by Amith2006 Since a unitary transformation preserves lengths and angle between the complex numbers in the 2 basis, doesn't it make sense to say its operates in a complex space?
in a complex space? i would say it operates on a complex space.