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Nathaniel Johnston

Introduction to Linear and Matrix Algebra 1st ed. 2021 Edition

by Nathaniel Johnston (Author)

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This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra.

Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software.

Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

ISBN-10

3030528138
ISBN-13

978-3030528133
Edition

1st ed. 2021
Publisher

Springer
Publication date

May 21, 2022
Language

English
Dimensions

7 x 1 x 10 inches
Print length

498 pages
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Nathaniel Johnston
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Editorial Reviews

Review

“The book is easy to read and requires almost no basic prior knowledge. … This is a good textbook on linear and matrix algebra. I would recommend this book to students who are learning linear algebra for the first time.” (Qing-Wen Wang, zbMATH 1481.15001, 2022)

From the Back Cover

This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra.

Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software.

Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Product details

Publisher ‏ : ‎ Springer; 1st ed. 2021 edition (May 21, 2022)
Language ‏ : ‎ English
Paperback ‏ : ‎ 498 pages
ISBN-10 ‏ : ‎ 3030528138
ISBN-13 ‏ : ‎ 978-3030528133
Item Weight ‏ : ‎ 2.08 pounds
Dimensions ‏ : ‎ 7 x 1 x 10 inches

Best Sellers Rank: #5,331,529 in Books (See Top 100 in Books)
- #1,348 in Linear Algebra (Books)
- #4,529 in Algebra & Trigonometry

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15 ratings

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Nathaniel Johnston

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Nathaniel Johnston is an Associate Professor in the Department of Mathematics and Computer Science at Mount Allison University in New Brunswick, Canada. He specializes in linear algebra, quantum information theory, and recreational mathematics.

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15 global ratings

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Amazon Customer

This is a gem of a math text!

Reviewed in the United States 🇺🇸 on May 4, 2022

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An effective mix of proof and practice problems. Very well written and very accessible, even for someone who last took a math class 45 years ago!

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L. Pedregosa

This book is well-written

Reviewed in the United States 🇺🇸 on June 27, 2021

Verified Purchase

I bought this book for my Linear Algebra class as a reference. I did not expect it is written really well. Very easy to understand. The author explains very well the definitions and theorems. He has so many great examples. I would recommend this book to professors and instructors of Linear Algebra. Many books in Linear Algebra were badly written and I can't understand it. But his one book is super easy to understand. Besides, the author also has a youtube video where he teaches this course. If you have his book and you follow his lectures, you will really fall in love with linear algebra.

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JAT

Best Linear Algebra intro book ever written

Reviewed in the United States 🇺🇸 on December 1, 2022

The author did a fantastic job. Clearly he put a lot of thought and effort writing this book and was bold to ignore many common choices made by most LA books at the same level.

To name some good choices:

* he wrote 2 books. This first one does cover a lot of material!! but, as I figured out long ago, traditional books of intro LA lack clarity in some points and this is a consequence of how much material the author aims to pack in one volume.

* how he deals with proofs. This is a very difficult topic in LA, and usually books goes to one of the extremes. This author was brilliant in this challenge. He has a very wise point of view of how much rigour is good enough for most serious learner at intro level. And he fulfiils the chosen level of rigor with exteme supportive style.

* how he deals with secondary content. He is very careful not too overload reader with more than needed to keep advancing on the material. With this in mind, every chapter have a reasonable amount of content as extra topics in the end. Most is useful to everyone and a minority only to some niche group. In any case, its a bless to be allowed to skip this in a first read as it keeps the core structure of the learning leaner and makes more accessible for the reader see bigger picture and connect the dots. This is really unique in this book compared to the competition.

* good exercises set and reasonable proportion of them with detailed solutions provided in the end of the book. Lots of exercises brings light to some secondary detail that helps the understanding of some core material, specially part of proofs that were skipped in the text but directed to the exercise number. With no exception, these cases allways are the ones with solutions provided in the book.

* videos!! his youtube channel has videos covering all materiall Honestly I barely watched some because I prefer written format and the book is that good.

Helpful

Top reviews from other countries

CSF

wonderful book

Reviewed in Spain 🇪🇸 on July 20, 2021

Verified Purchase

Excellent. The explanations are very clear and there are many examples.

NIC G.

Great Textbook on linear algebra

Reviewed in France 🇫🇷 on June 16, 2022

Verified Purchase

Excellent book dedicated to linear algebra, starting from the most elementary notions to raise the reader to the most complex ones (cfr notably the second book of the author which completes wonderfully this one).

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Introduction to Linear and Matrix Algebra 1st ed. 2021 Edition

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