Linear Algebra, Theory And Applications

Linear Algebra

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however.

This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants.

The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.

This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants.

The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.

Kenneth Kuttler

Saylor Foundation

Cut Rita Zahara

Creative Commons

Textbooks

Linear Algebra with Applications

Linear Algebra

This textbook is an introduction to the ideas and techniques of linear algebra for ﬁrst- or second-year students with a working knowledge of high school algebra. The contents have enough ﬂexibility to present

a traditional introduction to the subject, or to allow for a more applied course. Chapters

1–4 contain a onesemester course for beginners whereas Chapters 5–9 contain a second semester course (see the Suggested

Course Outlines below). The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix

A). Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. Calculus is not a prerequisite; places where it is mentioned may be omitted. As a rule, students of linear algebra learn by studying examples and solving problems. Accordingly, the book contains a variety of exercises (over 1200, many with multiple parts), ordered as to their difﬁculty.

In addition, more than 375 solved examples are included in the text, many of which are computational in nature. The examples are also used to motivate (and illustrate) concepts and theorems, carrying the student from concrete to abstract. While the treatment is rigorous, proofs are presented at a level appropriate to

the student and may be omitted with no loss of continuity. As a result, the book can be used to give a course that emphasizes computation and examples, or to give a more theoretical treatment (some longer

proofs are deferred to the end of the Section). Linear Algebra has application to the natural sciences, engineering, management, and the social sciences

as well as mathematics. Consequently, 18 optional “applications” sections are included in the text introducing topics as diverse as electrical networks, economic models, Markov chains, linear recurrences, systems of differential equations, and linear codes over ﬁnite ﬁelds. Additionally some applications (for example linear dynamical systems, and directed graphs) are introduced in context. The applications sections appear at the end of the relevant chapters to encourage students to browse.

a traditional introduction to the subject, or to allow for a more applied course. Chapters

1–4 contain a onesemester course for beginners whereas Chapters 5–9 contain a second semester course (see the Suggested

Course Outlines below). The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix

A). Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. Calculus is not a prerequisite; places where it is mentioned may be omitted. As a rule, students of linear algebra learn by studying examples and solving problems. Accordingly, the book contains a variety of exercises (over 1200, many with multiple parts), ordered as to their difﬁculty.

In addition, more than 375 solved examples are included in the text, many of which are computational in nature. The examples are also used to motivate (and illustrate) concepts and theorems, carrying the student from concrete to abstract. While the treatment is rigorous, proofs are presented at a level appropriate to

the student and may be omitted with no loss of continuity. As a result, the book can be used to give a course that emphasizes computation and examples, or to give a more theoretical treatment (some longer

proofs are deferred to the end of the Section). Linear Algebra has application to the natural sciences, engineering, management, and the social sciences

as well as mathematics. Consequently, 18 optional “applications” sections are included in the text introducing topics as diverse as electrical networks, economic models, Markov chains, linear recurrences, systems of differential equations, and linear codes over ﬁnite ﬁelds. Additionally some applications (for example linear dynamical systems, and directed graphs) are introduced in context. The applications sections appear at the end of the relevant chapters to encourage students to browse.

W. Keith Nicholson

lyryx with Open Texts

Cut Rita Zahara

Creative Commons

Textbooks

A First Course in Linear Algebra

Algebra

Linear Algebra

Mathematics

In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at “Answers to Odd-Numbered Exercises” section at the end of this book. This book is very useful for college students who studied Calculus I, and other students who want to review some linear algebra concepts before studying a second course in linear algebra. This book is available online for free in google books and ResearchGate in PDF format under a Creative Commons license.

Mohammed Kaabar

http://www.oercommons.org/courses/a-first-course-in-linear-algebra-study-guide-for-the-undergraduate-linear-algebra-course/view

CreateSpace, Charleston, SC

Taufiq A Gabi

Creative Commons