| 21. | A scaling in the most general sense is any affine transformation with a diagonalizable matrix.
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| 22. | Thus, every linear transformation is affine, but not every affine transformation is linear.
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| 23. | In contrast, a cardinal utility function is only unique up to positive affine transformation.
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| 24. | The inverse affine transformation is as follows:
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| 25. | This is the proper affine transformation for scaling by a factor of 1 / 2.
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| 26. | Affine transformations are applied to these polytopes, producing a description of a new execution order.
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| 27. | However, it is not equivariant under affine transformations of both the predictor and response variables.
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| 28. | Affine transformations of the plane are useful for studying equidissections, including similarities and linear maps.
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| 29. | The fact that affine transformations preserve equidissections also means that certain results can be easily generalized.
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| 30. | Affine transformations can theoretically add non-zero and complex utility aspects even to two player games.
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