2.18 should just be a linear transformation, not an automorphism

[jwmdykes]

Describe the mistake
For exercise 2.18, the linear maps f and g should just be linear transformations, not automorphisms. If f and g are automorphisms they're bijective, so their kernels are {0} and the question becomes trivial. For example in ker(f) = ker(g dot f) everything just cancels to the set {0} and there's no need to use the condition that g dot f = id_E.

Location

1. version
   Draft (2023-02-15) of “Mathematics for Machine Learning”.
2. Chapter
   chapter 2 exercises
3. page
   Page 68 in the ebook

Proposed solution
Change "Let f and g be two automorphisms on E" to "Let f and g be two endomorphisms on E."