The Maxwell equations are invariant under Lorentz transformations. It is the study of geometric properties that are invariant with respect to projective transformations. Metamorphosis serves as perhaps more than a metaphor for such transformations. The Laplacian is invariant under all Euclidean transformations&colon; rotations and translations. They later investigated W-curves, curves invariant under a group of projective transformations. This method also provides insight into how purely orthogonal/unitary transformations can obtain the SVD. The MLE is also invariant with respect to certain transformations of the data. Eigenvalues and eigenvectors feature prominently in the analysis of linear transformations. Ordinal utility functions are unique up to increasing monotone (or monotonic) transformations. They are classified and named by their orbits under affine transformations. Their behaviour under conformal transformations is more complicated. The set of possible canonical transformations is always very rich. The extension includes special conformal transformations and dilations. This simplifies many common tasks in Raku including input/output operations, list transformations, and parameter passing. They are often classified according to the cofactors that catalyze the transformations.