Advanced Linear Algebra, 3/e (Hardcover)

This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

這本研究生級教科書涵蓋了特別廣泛的主題。該書首先詳細討論了線性代數的基礎知識。接著探討了模組，並強調與向量空間的比較，並全面討論了內積空間、特徵值、特徵向量和有限維譜理論，最終達到了正規算子的有限維譜定理。新版已經修訂，並新增了一章關於QR分解、奇異值和偽逆，以及一章關於凸性、分離和線性系統的正解。