| 11. | A simple class of examples can be obtained by weakening the properties of unitary operators.
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| 12. | Note that the above decomposition of antiunitary operators contrasts with the spectral decomposition of unitary operators.
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| 13. | Unitary designs are especially useful in quantum computing since most operations are represented by unitary operators.
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| 14. | It thus defines a unitary operator.
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| 15. | Unitary operators are paramount to quantum theory, so unitary groups are important in particle physics.
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| 16. | Thus a unitary operator is a bounded linear operator which is both an isometry and a coisometry.
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| 17. | The complexification is invariant under taking adjoints, since consists of unitary operators and of positive operators.
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| 18. | For example, by properties of the Borel functional calculus, we see that for any unitary operator,
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| 19. | Since " T " is a unitary operator, its spectrum lies on the unit circle.
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| 20. | For example, the Fourier inversion theorem on shows that the Fourier transform is a unitary operator on.
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