CRex: What is the best approach to learning multilinear algebra knowing linear algebra?
This has been bugging me for years. I know linear algebra at a graduate level (from engineering courses, not from mathematics courses), but I cannot find anything that transitions to multilinear algebra. In the end, I’m interested in this topic from a purely mathematical point of view and from its applications to general relativity. Any help would be greatly appreciated.
Answers and Views:
Answer by spoon737
Check out the links in my source. They are books in pdf form on linear and multilinear algebra. You should have no trouble learning the subject if you start from the beginning. I’m assuming that if you have a graduate level understanding of linear algebra, then you should already be very comfortable with elementary abstract algebra. You’ll want to know your way around algebraic structures.
If you want to gain a better understanding of the usefulness of tensors (the main object of study in multilinear algebra) it would be good to know some differential geometry (which you would have to know anyways if you are studying relativity theory) and homological algebra. However, you can learn the subject without knowing either of these.