| Unitary Transformation |
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: where and are Hilbert spaces, such that : for all and in . A unitary transformation is an Isometry , as one can see by setting in this formula. In the case when and are the same space, a unitary transformation is an Automorphism of that Hilbert space, and then it is also called a Unitary Operator . A closely related notion is that of antiunitary transformation, which is a bijective function : between two Complex Hilbert spaces such that : for all and in , where the horizontal bar represents the Complex Conjugate . SEE ALSO |
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