This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined deter...
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Undergraduate Texts in Mathematics(共157册)，
这套丛书还有
《Linear Algebra》《Linear Algebra Through Geometry (Undergraduate Texts in Mathematics)》《Undergraduate Analysis》《Linear Programming and Its Applications》《Ideals, Varieties, and Algorithms》
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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![[美国] Sheldon Axler](https://img1.doubanio.com/view/personage/m/public/3b00f486efbfe9f15277095cf69e0478.jpg)
tianyikillua
团团就爱团团转
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人民邮电出版社2016版
1 有用 Backwater 2014-02-18 09:52:23
本科用线代教材 展开方式很独特
4 有用 万籁君 2015-01-31 05:04:13
review,对数学系学生应该非常简单，大一上高代时应该看。。。
0 有用 小鹿鹿想吃油条 2015-11-11 11:59:56
I love math 113
0 有用 sevennick 2012-09-16 05:44:17
最喜欢的线性代数教材。开学前又拿它过了一遍，温故知新。
3 有用 你的友邻 2013-03-30 17:44:26
主要关注矩阵的线性映射，直到最后一章才提到了关于矩阵自身的迹和行列式。另外，我是看了这个链接之后才发觉有这本书的。http://www.mysanco.com/wenda/index.php?class=discuss&action=question_item&questionid=1693