The definition of the tensor product and existence/uniqueness/associativity properties.

I know, this is perhaps not a single theorem but in my eyes one of the most useful "elemetary" concepts. Personally, I had two semesters of linear algebra without mentioning the tensor product. And from this I suffered for a long time during my further studies. Now it is my first homework/exercise for students in my lectures (e.g. diff geo).

If the student is really clever, one can even do something like the tensor algebra in these 30 min.

The definition of the tensor product and existence/uniqueness/associativity properties.

I know, this is perhaps not a single theorem but in my eyes one of the most useful "elementary" concepts. Personally, I had two semesters of linear algebra without mentioning the tensor product. And from this I suffered for a long time during my further studies. Now it is my first homework/exercise for students in my lectures (e.g. diff geo).

If the student is really clever, one can even do something like the tensor algebra in these 30 min.