Linear Algebra I built a complete, working toolkit: vector spaces, subspaces, span, independence, basis, dimension, linear transformations, rank-nullity, change of basis, determinants, inner products, orthogonality, Gram–Schmidt, and eigenvalues, all the way through diagonalizing a symmetric matrix with an orthogonal eigenvector basis. Every one of those ideas is assumed complete on day one of this course — sections 1 through 7 of this chapter exist only to put a name back on each one and hand back a handful of review questions, not to reteach anything.
Sections 8 and 9 are different: they genuinely teach. Complex numbers and polynomial factorization both got a full treatment in College Algebra, but never at the depth a course about eigenvalues over \mathbb C actually needs — conjugate pairs, the complex inner product's conjugate-symmetry convention, and exactly how a polynomial's factorization over \mathbb R differs from its factorization over \mathbb C all get a focused pass here, because chapter 06 leans on every one of them from its very first page.
The throughline connecting all nine sections is the picture on this chapter's own cover: a 2×2 matrix with no real eigenvector at all. Linear Algebra I's eigenvalue chapter noted this case existed and moved past it. This course starts by asking what a "highway that doesn't exist on the real map" actually means, and spends its next twelve chapters building the machinery — complex vector spaces, the spectral theorem, canonical forms — that answers the question completely.