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Unitary transformation

by Amith2006
Tags: transformation, unitary
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Amith2006
#1
Nov24-08, 01:41 PM
P: 421
Can it be said that similarity transformation is a transformation in real space while unitary transformation is a transformation in complex space?
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ice109
#2
Nov24-08, 01:44 PM
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.
Amith2006
#3
Nov24-08, 02:39 PM
P: 421
Quote Quote by ice109 View Post
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?

ice109
#4
Nov24-08, 03:08 PM
P: 1,705
Unitary transformation

Quote Quote by Amith2006 View Post
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.

what is your native language?
Amith2006
#5
Nov24-08, 03:25 PM
P: 421
Quote Quote by ice109 View Post
in a complex space? i would say it operates on a complex space.

what is your native language?
Well, not English but this was just a typographic error buddy. So, what do u say about unitary transformation- operating on a complex space?
ice109
#6
Nov24-08, 04:21 PM
P: 1,705
Quote Quote by Amith2006 View Post
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.


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