| 1. | The converse is also true : orthogonal matrices imply orthogonal transformations.
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| 2. | In particular, orthogonal transformations map orthonormal bases to orthonormal bases.
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| 3. | The inverse of an orthogonal transformation is another orthogonal transformation.
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| 4. | The inverse of an orthogonal transformation is another orthogonal transformation.
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| 5. | These orthogonal transformations form a group under composition, the orthogonal group.
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| 6. | We say central fields are orthogonal transformations around 0.
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| 7. | From the previous table, orthogonal transformations of covectors and contravectors are identical.
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| 8. | :: That's only orthogonal transformations.
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| 9. | Hence a set of factors and factor loadings is unique only up to orthogonal transformation.
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| 10. | Converting a tensor's components from one such basis to another is through an orthogonal transformation.
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