| In 1911 he established his theorems on the invariance of the dimension of a manifold under continuous invertible transformations. |
| But because cryptographic functions must be invertible, must be fast to compute, and should have small key size and memory requirements, linear functions are irresistible. |
| This normally guarantees a Jacobien, i.e. an initial invertible system base. |
| It can be proved that a Dedekind domain is equivalent to an integral domain in which every proper fractional ideal is invertible. |
| Projective transformations, which are invertible linear changes of homogeneous coordinates, are given by matrix multiplication. |
| What follows is not a strict fugue, but a fugato in five-part invertible counterpoint. |
