One Interactive Map: Algebra → Spectral Theory → Geometry → Data Applications
Blue arrows show a natural learning path. The inner-product portion is integrated into the same diagram rather than placed on a separate page.
Course narrative
Linear algebra begins with solving linear systems and organizing computations with matrices. Vector spaces and linear transformations explain why these computations work. Bases and coordinates allow abstract objects to be represented by columns and matrices. Eigenvalues and eigenspaces reveal invariant directions, leading to diagonalization, Jordan form, Perron–Frobenius theory, Markov chains, dynamical systems, and PageRank. Inner product spaces add geometry: length, angle, orthogonality, projection, least squares, QR factorization, spectral decomposition, SVD, PCA, and FFT.
Computational start:
linear systems, matrices, row reduction.
linear systems, matrices, row reduction.
Abstract structure:
vector spaces, bases, coordinates, linear maps.
vector spaces, bases, coordinates, linear maps.
Spectral structure:
eigenvalues, diagonalization, Jordan form.
eigenvalues, diagonalization, Jordan form.
Geometric/data tools:
inner products, projections, QR, SVD, PCA.
inner products, projections, QR, SVD, PCA.