Similarity vs. Unitary Transformations

Amith2006
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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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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.
 
ice109 said:
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?
 
Amith2006 said:
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?
 
ice109 said:
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?
 
Amith2006 said:
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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