Abstract Algebra 59: Analogy between group homomorphisms and linear transformations (linear algebra)

Abstract Algebra 59: Analogy between group homomorphisms and linear transformations (linear algebra)

Abstract: Linear transformations are group homomorphisms, but they also preserve additional vector space structure. Kernels of linear transformations are just as important as kernels of group homomorphisms. "Modding out by a kernel" is perhaps easier to visualize in the context of linear algebra. We make several loose analogies related to the Rank-Nullity Theorem (linear algebra) and the First Isomorphism Theorem (group theory). The tone of this video is meant to be loose, imprecise, non-rigorous, visual, and motivating.

This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University: