- Linear Algebra A Solution Manual for Axler(1997),Lax(2007), andRoman (2008) Jianfei Shen School of Economics, The University of New South Wales Sydney, Australia.
- Linear Algebra Done Right (3rd ed.) (Undergraduate Texts in Mathematics series) by Sheldon Axler. Read online, or download in DRM-free PDF (digitally watermarked) format. 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.
Linear Algebra Done Wrong
Linear Algebra Done Right by Sheldon Axler Summary
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.
What is particularly done 'wrong' in the book? Before answering these questions, let me first describe the target audience of this text. This book appeared as lecture notes for the course 'Honors Linear Algebra'. It supposed to be a first linear algebra course for mathematically advanced students. It is intended for a student who, while not yet.
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