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.
Writing for undergraduate students of mathematics, science, engineering, or computer science who already know how to work with matrices and how to use them to solve systems of linear equations, Dillon, explores the algebra underlying and emanating from a study of systems of linear equations and matrix manipulation. Her approach is proof-based with an emphasis on algebraic foundations. As important at applications and software are, she says, her aim is to set out the mathematics that supports the tools students will need for applications, inside and outside mathematics, with and without the help of machine computing. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
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