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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?
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.
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?
ice109 said:in a complex space? i would say it operates on a complex space.
what is your native language?
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?
Similarity transformations are transformations that preserve the shape and relative orientation of an object, while unitary transformations preserve the length and angle relationships of vectors. In other words, similarity transformations change the size and orientation of an object, while unitary transformations only change its orientation.
Yes, a transformation can be both similarity and unitary. This means that it preserves both shape and relative orientation, as well as length and angle relationships.
A dilation, or stretching, of an object is an example of a similarity transformation. This changes the size of the object while keeping its shape and orientation the same.
A rotation of an object in 2-D space is an example of a unitary transformation. This changes the orientation of the object while keeping the lengths and angles between its components the same.
Similarity and unitary transformations are useful in many areas of science, including physics, engineering, and computer graphics. They allow us to manipulate and analyze objects and data in a way that preserves important relationships and properties, making it easier to study and understand complex systems.