Neri F. Linear Algebra for Computational Sciences...2ed 2019

Textbook in PDF format

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.
Basic Mathematical Thinking
Matrices
Systems of Linear Equations
Geometric Vectors
Complex Numbers and Polynomials
An Introduction to Geometric Algebra and Conics
An Overview on Algebraic Structures
Vector Spaces
An Introduction to Inner Product Spaces: Euclidean Spaces
Linear Mappings
An Introduction to Computational Complexity
Graph Theory
Applied Linear Algebra: Electrical Networks