Have you ever encountered a college-level textbook with a title like this one? *Linear Algebra Done Wrong* is the title of an honors linear algebra textbook. The premise is that students are mathematically advanced, who are willing to study rigorous mathematics presented in a non-traditional format – no “cookbook style” here. Students will be introduced to *rigorous* proof, formal definitions and begin their transition to modern theoretical (abstract) mathematics study.

According to the author, Sergei Treil, he is somewhat unique among linear algebra textbook authors in that he is not an algebraist. His text puts more emphasis on topics important for analysis, geometry, and probability, among others. His Brown University page shows pictures of him braving white-water rapids in a kayak and on a riverboard. So, is it any wonder that this mathematics professor would take a different approach to presenting this topic?

Treil, explains in far greater detail what makes his linear algebra text “wrong.” It’s simply been way too many years since I took a linear algebra course and I have to admit that most of his explanation is way over my head. Hopefully, for students currently studying this topic, it will be more meaningful and his approach to teaching linear algebra will entice you to explore more of his work.

## Contents of *Linear Algebra Done Wrong*

- Basic Notations
- Systems of linear equations
- Determinants
- Introduction to spectral theory (eigenvalues and eigenvectors)
- Inner product spaces
- Structure of operators in inner product spaces
- Bilinear and quadratic forms
- Dual spaces and tensors
- Advanced spectral theory

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Linear Algebra Done Wrong