Linear Algebra Done Right

Linear Algebra Done Right, now in its second edition, is crafted for math majors and graduate students seeking a deeper understanding of linear algebra. Eschewing the early introduction of determinants, the text focuses on unraveling the structure of linear operators on vector spaces, ensuring that core concepts are grasped with clarity and precision. Beginning with fundamental ideas such as vector spaces, linear independence, basis, and dimension, the book carefully guides readers through progressively sophisticated topics. Early chapters introduce inner-product spaces, leading naturally into the finite-dimensional spectral theorem, while later sections explore advanced themes like self-adjoint and normal operators. This edition enriches the learning experience with a new segment on orthogonal projections and minimization problems, along with revised proofs, updated examples, and a broad spectrum of exercises designed to reinforce and extend understanding of linear algebra.