Invertible function

A linear operator T is invertible if

 det T ≠ 0.

An affine function is invertible is the corresponding linear operator is invertible. For example, supose

 T( u, v ) = | 1  3 | | u | + | 1 |
             | 2  1 | | v |   | 1 |,

then

 | det T | = | 1  3 | = | 1 - 6 | = 5.
             | 2  1 |