# Unitary transformation

1. ### Amith2006

421
Can it be said that similarity transformation is a transformation in real space while unitary transformation is a transformation in complex space?

2. ### ice109

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.

3. ### Amith2006

421
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?

4. ### ice109

in a complex space? i would say it operates on a complex space.