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 moti...
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.
Sheldon Axler is Dean of the College of Science & Engineering at San Francisco State University. He has authored many well-received books including Precalculus: A Prelude to Calculus, Algebra & Trigonometry, College Algebra, A Glimpse at Hilbert Space Operators, Harmonic Function Theory, and Holomorphic Spaces.
Undergraduate Texts in Mathematics(共146册)，
这套丛书还有
《Mathematics and Its History》《From Fermat to Minkowski》《Basic Topology》《Linear Algebra》《Multivariable Calculus with Applications》
等
。
以下内容是初读此书时写的，有些内容经过一段时间的学习发现许多东西并不准确（且幼稚）但也不想修改。如果是做纯数research（phd之类的）这只能是基础中的基础（找professor时候说我认真学完了这本书他鄙视了一番，you should read xxxx, not liike Sheldon Axler），属于入门...
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tianyikillua
Springer1997版
团团就爱团团转
人民邮电出版社2009版
Moeyfish
Springer1997版
OrganicMilk
Springer International Publishing2014版
豆友207282466
人民邮电出版社2016版
0 有用 Foe 2017-03-18 11:24:24
温习线代用的，视角和原来学的完全不一样...
0 有用 gtianp 2020-11-18 14:51:19
做完了几乎所有习题，几个重要的结论挪到了习题中，比方说上三角阵对角线上是各特征值依其重数重复。证明的部分有的会给出是如何想到的，受到了什么启发。这一点我认为比一个漂亮的证明更重要。总的来说这本书很“代数”而不“算术”。让行列式和矩阵当配角，把线性代数从繁冗的计算中解脱出来，从线性空间和线性变换的角度出发，会有一种一览众山小的感觉。
0 有用 gtianp 2020-11-18 14:51:19
做完了几乎所有习题，几个重要的结论挪到了习题中，比方说上三角阵对角线上是各特征值依其重数重复。证明的部分有的会给出是如何想到的，受到了什么启发。这一点我认为比一个漂亮的证明更重要。总的来说这本书很“代数”而不“算术”。让行列式和矩阵当配角，把线性代数从繁冗的计算中解脱出来，从线性空间和线性变换的角度出发，会有一种一览众山小的感觉。
0 有用 Foe 2017-03-18 11:24:24
温习线代用的，视角和原来学的完全不一样...