Normal forms of semilinear operators (Q1818424)

The author discusses normal forms of semilinear mappings of a finite-dimensional vector space into itself; the ground field is allowed to be skew. In contrast to a previous article by him [Boll. Unione Mat. Ital., VII. Ser., A 4, No. 2, 209-218 (1990; Zbl 0709.15003)] on the same subject, the present approach is based only on linear algebra and not on results from representation theory. A number of explicit examples illustrates that certain well-known theorems on linear endomorphisms cannot be carried over to semilinear mappings.