num_pages: 0
description: This textbook is directed towards students who are familiar with matrices and their use in solving systems of linear equations. The emphasis is on the algebra supporting the ideas that make linear algebra so important both in theoretical and practical applications. The narrative is written to bring along students who may be new to the level of abstraction essential to a working understanding of linear algebra. The determinant is used throughout placed in some historical perspective and defined several different ways including in the context of exterior algebras. The text details proof of the existence of a basis for an arbitrary vector space and addresses vector spaces over arbitrary fields. It develops LU-factorization Jordan canonical form and real and complex inner product spaces. It includes examples of inner product spaces of continuous complex functions on a real interval as well as the background material that students may need in order to follow those discussions. Special classes of matrices make an entrance early in the text and subsequently appear throughout. The last chapter of the book introduces the classical groups.
language: None
title: Linear Algebra: Vector Spaces and Linear Transformations
publisher: American Mathematical Society