Can it be said that similarity transformation is a transformation in real space while unitary transformation is a transformation in complex space?
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.
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?
Well, not English but this was just a typographic error buddy. So, what do u say about unitary transformation- operating on a complex space?
buddy don't get mad, i was wondering what it was so if i spoke it i could tell you in that language. i don't say anything about a unitary operation operating on a complex space.