Sheldon Axler
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.
Sheldon Axler, Measure, Integration & Real Analysis, Springer GTM 282, 2020. Open access — the free electronic edition lives at measure.axler.net.
Covers Riemann integration and its limitations, measures and their construction, integration, differentiation, product measures, Banach and Hilbert spaces, \(L^p\) spaces, real and complex measures, spectral theory for compact operators, and probability measures. Exercises sit at the end of each section (1A, 1B, …), with no printed answers.
Solutions to every exercise live at Solutions to Axler’s Measure, Integration & Real Analysis.