The essence of linear algebra is vector spaces and linear transformations. It's not entirely impossible (although probably way more difficult) to learn it witho

The essence of linear algebra is vector spaces and linear transformations. It's not entirely impossible (although probably way more difficult) to learn it without reference to Euclidean spaces and geometric reasoning. Should be called "The intuition for linear algebra". But heck, the whole reason we have and teach the mathematical method is that intuition either breaks down in interesting cases (e.g. stochastic integrais versus "an area under a curve" integrals) or limits you (linear algebra in function spaces, etc). It's a nitpick. I love 3b1b.