Fun with polynomials and linear algebra; or, slight abstract nonsense
Summary
A dense set of notes exploring how many standard constructions in algebra can be done purely in linear algebra language. It covers vector spaces, quotients V/W, V/Wp ≃ Rp, and an abstract, polynomial-CRT-like decomposition for subspaces, drawing connections to the division algorithm and Bezout’s lemma, and includes a 'basis view' via stacked matrices.