Linear algebra as we learn it as undergraduates usually holds for any field (even though we usually learn it for the complex, or real, numbers).


I am looking for a list of concepts, and results, in linear algebra that actually depend on the choice of field.


To start I propose the notion of an complex valued inner product. Here the anti-linear axiom requires an involution on the field.



Results in linear algebra that depend on the choice of field
The existence of Chevalley–Jordan decompositions depends on the perfectness of the field.


