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Mathematics LibreTexts

Linear Algebra (Schilling, Nachtergaele and Lankham)

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As an Introduction to Abstract Mathematics is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular the concept of proofs in the setting of linear algebra. Typically such a student will have taken calculus, though the only prerequisite is suitable mathematical maturity. The purpose of this book is to bridge the gap between the more conceptual and computational oriented lower division undergraduate classes to the more abstract oriented upper division classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

Thumbnail: A linear system in three variables determines a collection of planes. The intersection point is the solution. (CC BY-SA 4.0; Fred the Oyster via Wikipedia)


This page titled Linear Algebra (Schilling, Nachtergaele and Lankham) is shared under a not declared license and was authored, remixed, and/or curated by Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling.

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