
Linear Algebra
Vector Spaces and Linear Transformations
Meighan I. Dillon(Author)
American Mathematical Society (Publisher)
Published on 30. January 2023
Book
Paperback/Softback
367 pages
978-1-4704-6986-3 (ISBN)
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
272 gr
ISBN-13
978-1-4704-6986-3 (9781470469863)
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Schweitzer Classification
Person
Meighan I. Dillon, Kennesaw State University, Marietta, GA.
Content
Introduction
Vector spaces
Linear transformations and subspaces
Matrices and coordinates
Systems of linear equations
Introductions
The determinant is a multilinear mapping
Inner product spaces
The life of a linear operator
Similarity
$GL_n(\mathbb{F})$ and friends
Background review
$\mathbb{R}^2$ and $\mathbb{R}^3$
More set theory
Infinite dimension
Bibliography
Index
Vector spaces
Linear transformations and subspaces
Matrices and coordinates
Systems of linear equations
Introductions
The determinant is a multilinear mapping
Inner product spaces
The life of a linear operator
Similarity
$GL_n(\mathbb{F})$ and friends
Background review
$\mathbb{R}^2$ and $\mathbb{R}^3$
More set theory
Infinite dimension
Bibliography
Index