MATRIX SPACE · OPEN ACADEMIC NOTES
A continuously maintained set of research and study notes covering matrix analysis, numerical linear algebra, and randomized matrix computations — with original figures, interactive demonstrations, and a curated lecture library.
Three reading tracks, one interactive playground, and a video shelf.
Self-contained notes on the singular value decomposition, eigenvalue theory, and iterative Krylov-subspace solvers, with theorem boxes and figures.
Start with the SVD →How random projections turn low-rank matrix approximation into a near-linear-time computation, with illustrative numerical observations.
Randomized matrix approximation →Drag the entries of a 2×2 matrix and watch the plane deform; run the power method and watch the eigenvalue estimate converge.
Open the demos →Embedded lectures that build geometric intuition for vectors, transformations, determinants, and column spaces.
Browse the videos →Every linear map is a rotation, an axis-aligned stretch, and another rotation. This is the singular value decomposition.
Figure 1. The three geometric stages of the SVD for a 2×2 matrix. The full story — including why this decomposition exists and why it gives the best possible rank-k approximation — is in the SVD notes.
The notes are revised whenever an error is found or a section is expanded.