Applied Multivariate Statistical Analysis (6th edition, Pearson, 2007) by Johnson and Wichern — the classic applied treatment of multivariate methods: the multivariate normal, inference about mean vectors, MANOVA, covariance structure, principal components, factor analysis, canonical correlation, discrimination and classification, and clustering, grounded throughout in worked data examples.
Linear-Algebra
2026-09-27
Kenneth Hoffman and Ray Kunze, Linear Algebra, Prentice-Hall, 1961 (first edition). The rigorous MIT text: linear equations and vector spaces, linear transformations, polynomials, determinants, elementary canonical forms, the rational and Jordan forms, inner product spaces, and bilinear forms. A 1961 Prentice-Hall hardcover copy.
Worked solutions to all 732 exercises in the fourth edition of Sheldon Axler's Linear Algebra Done Right — vector spaces, finite-dimensional vector spaces, linear maps, polynomials, eigenvalues and eigenvectors, inner product spaces, operators on inner product and complex vector spaces, and multilinear algebra and determinants.
Sheldon Axler, Linear Algebra Done Right, 4th edition, Springer UTM, 2024. Open access — the free electronic edition lives at linear.axler.net.
The determinant-last treatment of linear algebra: vector spaces, linear maps, polynomials, eigenvalues and eigenvectors, inner product spaces, operators on inner product spaces, operators on complex and real vector spaces, multilinear algebra and determinants. Exercises per section (1A, 1B, …), no printed answers. The 4th edition renumbers and extends the 3rd edition’s exercise sets.
pca is the linear algebra exam question that escaped into industry. given a cloud of points in \(\mathbb{R}^d\), it finds the orthogonal directions along which the cloud spreads the most, and lets you throw away the rest. 𐃏 two apparently different questions — “which directions carry the most variance?” and “which subspace loses the least when i project onto it?” — turn out to have the same answer, and that answer is an eigendecomposition.
As is tradition, the prize pool has increased (to $300 this year).
I have collapsed first and second place into a winner-takes-all arrangement (c’est la vie).
Furthermore, there are additional changes to the structure of this Game:
- you must now pass the problem set to be awarded the prize money;
- you may submit your solutions to the problem set at any point in the future;
- if you plagiarise work, I reserve the right to ban you from all subsequent competitions — grim trigger
- the problem and solution set will now be courteously supported by MathJaX, TikZ, and my own JavaScript
- Good luck!
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Links
Structure
Most notably, the structure from this year has changed. Instead of just offering a single PDF and then writing up solutions on this site, the problems themselves are accessible from below and once 2025 transpires, my solutions will be available as toggled nested environments.