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