# Linear Algebra for Computational Sciences and Engineering

Textbook

1. Front Matter
Pages i-xxii
2. ### Foundations of Linear Algebra

1. Front Matter
Pages 1-1
2. Ferrante Neri
Pages 3-13
3. Ferrante Neri
Pages 15-39
4. Ferrante Neri
Pages 41-96
5. Ferrante Neri
Pages 97-129
6. Ferrante Neri
Pages 131-158
7. Ferrante Neri
Pages 159-207
3. ### Elements of Linear Algebra

1. Front Matter
Pages 209-209
2. Ferrante Neri
Pages 211-231
3. Ferrante Neri
Pages 233-281
4. Ferrante Neri
Pages 283-347
5. Ferrante Neri
Pages 349-362
6. Ferrante Neri
Pages 363-430
7. Ferrante Neri
Pages 431-449
4. Back Matter
Pages 451-464

### Introduction

This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory.

It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who need a theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.

### Keywords

Boolean algebra Linear mappings Set theory Matrices Systems of linear equations Vectors Complex numbers Polynomials Geometry Conics Vector spaces Graph theory Electrical networks Electrical circuits

#### Authors and affiliations

1. 1.Centre for Computational IntelligenceDe Montfort UniversityLeicesterUnited Kingdom

Ferrante Neri received a Master's degree and a PhD in Electrical Engineering from the Technical University of Bari, Italy, in 2002 and 2007 respectively. In 2007, he also received a PhD in Scientific Computing and Optimization from University of Jyväskylä, Finland. He was appointed Assistant Professor at the Department of Mathematical Information Technology at the University  of Jyväskylä, Finland in 2007, and in 2009  as a Research Fellow with Academy of Finland. Neri moved to De Montfort University, United Kingdom in 2012, where he was appointed Reader in Computational Intelligence. Since 2013, he is Full Professor of Computational Intelligence Optimisation at De Montfort University, United Kingdom. He is also Visiting Professor  at the University  of Jyväskylä, Finland. Currently, he teaches linear algebra and discrete mathematics at De Montfort University. His research interests include algorithmics, metaheuristic optimisation, scalability in optimisation and large scale problems.

### Bibliographic information

• Book Title Linear Algebra for Computational Sciences and Engineering
• Authors Ferrante Neri
• DOI https://doi.org/10.1007/978-3-319-40341-0
• Copyright Information Springer International Publishing Switzerland 2016
• Publisher Name Springer, Cham
• eBook Packages Computer Science Computer Science (R0)
• Hardcover ISBN 978-3-319-40339-7
• eBook ISBN 978-3-319-40341-0
• Edition Number 1
• Number of Pages XXII, 464
• Number of Illustrations 8 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site

## Reviews

“In this book, Ferrante Neri elaborates on this algebraic background, providing a very good starting point for undergraduate students who wish to gain a basic understanding of the theories behind the most exciting parts of contemporary information technology (IT) technologies. … As Neri’s work is a self-contained textbook, everything is explained from scratch and all of the chapters finish with exercises to test the reader’s understanding of just the presented material.” (Piotr Cholda, Computing Reviews, May, 2017)

“This is a nice, compact treatment, especially for those individuals who have yet to take an abstract algebra course. … The topic of computational complexity is a welcome addition to any text on linear algebra. … All in all, this is a thorough, carefully written text that can be utilized for any introductory linear algebra course. Summing Up: Recommended. Lower- and upper-division undergraduates.” (R. L. Pour, Choice, Vol. 54 (6), February, 2017)