| Chapter | Topic | Example Problem Flavor | | :--- | :--- | :--- | | 1 | Scalars | Why do we need fields of characteristic not 2? | | 2 | Vector Spaces | Linear dependence without coordinates. | | 3 | Linear Transformations | The algebra of linear maps. | | 4 | Polynomials | Minimal polynomials and the Cayley-Hamilton theorem. | | 5 | Determinants | The only multilinear alternating form. | | 6 | Eigenvalues | Invariant subspaces and triangulation. | | 7 | Inner Product Spaces | Orthogonality and adjoints. | | 8 | Normality | Unitary and self-adjoint operators. | | 9 | Spectral Theorem | The crown jewel of finite-dimensional linear algebra. |
If your library only has a physical copy, request an ILL. Some libraries will scan the entire book for you as a PDF for personal educational use under fair use provisions. linear algebra problem book paul r. halmos pdf
The book is written in a Socratic dialogue style. Each chapter begins with a set of core problems. As you struggle through them, Halmos guides you via hints and preceding discussions. You don't just learn what a vector space is; you discover why the axioms are necessary by solving problems that would fail without them. | Chapter | Topic | Example Problem Flavor
The book is divided into 13 chapters, each a modular collection of problems. Here are the highlights: | | 4 | Polynomials | Minimal polynomials