Linear Algebra Done Right (Hardcover) 3/e

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.

The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.

No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

這本暢銷教科書是為大學數學專業的本科生和研究生設計的第二門線性代數課程。這裡採用了一種新穎的方法，將行列式放在了書的末尾。本書的重點是線性代數的核心目標：理解有限維向量空間上的線性算子的結構。作者非常謹慎地引導概念並簡化證明。每章都有各種有趣的練習題，幫助學生理解和操作線性代數的對象。

第三版在整本書中進行了重大改進和修訂。與上一版相比，增加了300多個新的練習題。增加了許多新的例子來說明線性代數的關鍵思想。書中新增的主題包括乘積空間、商空間和對偶空間。美觀的新格式在印刷和電子版本中都呈現出非常愉悅的外觀。

除了對適當的數學成熟度的要求外，本書不需要其他先備知識。因此，本書從討論向量空間、線性獨立性、張成、基底和維度開始。然後介紹線性映射、特徵值和特徵向量。引入內積空間，引出有限維譜定理及其結果。然後使用廣義特徵向量來深入了解線性算子的結構。