A Second Course in Linear Algebra

This is a course in linear algebra for students who have had a standard first course (vector space, linear map, characteristic polynomial). We’ll emphasize coordinate-free constructions and universal properties as much as possible. Among the topics we’ll study are sum, product and quotient spaces; duality (kernel, cokernel); tensor product (Hilbert’s third problem, differential form); homological algebra (exact sequence, snake lemma); normal forms (Frobenius, Weyr, Smith) and invariant factors. If there are sufficient time and interest, we might explore other topics, such as geometric algebra, control theory (pole placement) and/or tropical linear algebra.