This short but rigorous book approaches the main ideas of linear algebra through carefully selected examples and relevant applications. It is intended for students with various interests in mathematics, as well as established scientists seeking to refresh their basic mathematical culture.

The book is also a good introduction to functional analysis and quantum theory since it discusses the general principles of linear algebra without finiteness assumptions.

Contents:

• Linear Systems: Elimination Method
• Vector Spaces
• Matrix Multiplication
• Linear Maps
• The Rank Theorem
• Eigenvectors and Eigenvalues
• Inner-Product Spaces
• Symmetric Operators
• Duality
• Determinants
• Applications
• Normal Operators

“I found several interesting and unusual problems that I'll probably use in exams ... I recommend this book as supplementary reading for anyone interested in Linear Algebra, specially students looking for a change from their textbook. Instructors will find here some interesting material that they can use in class and in exams. I did.”

“I recommend this book as a reference for teachers who need to find interesting examples that would motivate the study of Linear Algebra.”

“The author has succeeded in writing an introduction to linear algebra using a novel and very interesting and instructive approach ... this book is a valuable addition to the library of linear algebra texts and can be thoroughly recommended to any student seeking a deeper understanding of linear algebraic concepts.”