| 1. | An orthogonal matrix " Q " is necessarily reflection.
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| 2. | The real analogue of a unitary matrix is an orthogonal matrix.
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| 3. | Where is a diagonal matrix and is an orthogonal matrix.
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| 4. | This can be achieved by the following orthogonal matrix ( with unit determinant)
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| 5. | As a linear transformation, every special orthogonal matrix acts as a rotation.
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| 6. | The determinant of any orthogonal matrix is either or.
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| 7. | The orthogonal matrix corresponding to the above reflection is the matrix whose entries are
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| 8. | Then, any orthogonal matrix is either a rotation or an improper rotation.
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| 9. | Where O is an orthogonal matrix and P is a 4-vector.
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| 10. | Thus every rotation can be represented uniquely by an orthogonal matrix with unit determinant.
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