Linear Algebra Done Wrong (2004)
Linear Algebra Done Wrong by Sergei Treil is a free textbook for advanced students, focusing on finite-dimensional vector spaces and emphasizing analysis, geometry, and probability, with updates in the 2017 version.
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Linear Algebra Done Wrong, authored by Sergei Treil, serves as a textbook for an honors linear algebra course aimed at mathematically advanced students. The book is designed to introduce students to rigorous mathematics, moving beyond the "cookbook style" of traditional calculus courses. It emphasizes a blend of elementary concepts and concrete examples while focusing on topics relevant to analysis, geometry, and probability, rather than traditional algebraic topics. The text restricts its scope to finite-dimensional vector spaces over real or complex fields, intentionally omitting infinite-dimensional spaces to avoid the complexities of functional analysis. The book is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License, allowing free use for non-commercial purposes, including teaching and studying. The September 2017 version includes corrections of numerous typos and updates to exercises, as well as expanded sections on non-orthogonal orthogonalization and singular value decomposition. The book is available for download in PDF format, along with previous versions and errata.
- The book targets mathematically advanced students for a rigorous introduction to linear algebra.
- It focuses on finite-dimensional vector spaces over real or complex fields.
- The text is available for free under a Creative Commons license for non-commercial use.
- The September 2017 version includes corrections and updates to exercises.
- It emphasizes applications relevant to analysis, geometry, and probability rather than traditional algebra topics.
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8 commentsDoes he ever answer this question? It's posed at the start of the book, but then immediately ignored.
Linear Algebra Done Wrong [pdf] - https://news.ycombinator.com/item?id=999494 - Dec 2009 (12 comments)
Every lecture was so eye opening. I couldn't believe that linear algebra could be taught in such a context with such a variety of application domains.
The lectures are all available online with the assignments : https://ee263.stanford.edu/archive/
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