Softcover ISBN:  9781470448714 
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eBook ISBN:  9781470451493 
Product Code:  CLN/29.E 
List Price:  $51.00 
MAA Member Price:  $45.90 
AMS Member Price:  $40.80 
Sale Price:  $33.15 
Softcover ISBN:  9781470448714 
eBook: ISBN:  9781470451493 
Product Code:  CLN/29.B 
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AMS Member Price:  $81.60$61.20 
Sale Price:  $66.30$49.73 
Softcover ISBN:  9781470448714 
Product Code:  CLN/29 
List Price:  $51.00 
MAA Member Price:  $45.90 
AMS Member Price:  $40.80 
Sale Price:  $33.15 
eBook ISBN:  9781470451493 
Product Code:  CLN/29.E 
List Price:  $51.00 
MAA Member Price:  $45.90 
AMS Member Price:  $40.80 
Sale Price:  $33.15 
Softcover ISBN:  9781470448714 
eBook ISBN:  9781470451493 
Product Code:  CLN/29.B 
List Price:  $102.00$76.50 
MAA Member Price:  $91.80$68.85 
AMS Member Price:  $81.60$61.20 
Sale Price:  $66.30$49.73 

Book DetailsCourant Lecture NotesVolume: 29; 2019; 261 ppMSC: Primary 97; 15; 40; 20;
This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise.
This first volume reexamines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are wellcrafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.ReadershipUndergraduate and graduate students interested in an advanced understanding of linear algebra for graduate studies.
This item is also available as part of a set: 
Table of Contents

Chapters

Vector Spaces Over a Field $\mathbb {K}$

Linear Operators $T: V \to W$

Duality and the Dual Space $V^*$

Determinants

The Diagonalization Problem

Inner Product Spaces


Additional Material

Reviews

The book is nicely written at an appropriate level of sophistication, and there is a good selection of exercises, both imbedded in the text itself and collected, section by section, at the end of each chapter.
Mark Hunacek, Iowa State University 
Students would benefit immensely from a course based on a textbook like this one.
Fernando Gouvêa, MAA Reviews


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
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This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise.
This first volume reexamines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are wellcrafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.
Undergraduate and graduate students interested in an advanced understanding of linear algebra for graduate studies.

Chapters

Vector Spaces Over a Field $\mathbb {K}$

Linear Operators $T: V \to W$

Duality and the Dual Space $V^*$

Determinants

The Diagonalization Problem

Inner Product Spaces

The book is nicely written at an appropriate level of sophistication, and there is a good selection of exercises, both imbedded in the text itself and collected, section by section, at the end of each chapter.
Mark Hunacek, Iowa State University 
Students would benefit immensely from a course based on a textbook like this one.
Fernando Gouvêa, MAA Reviews