% Abstract
This book contains lessons on linear algebra written in a style that is jargon-free and to the point.
Each lesson covers one concept at the depth required for a first-year university-level course.
The main focus of the book is to show the intricate connections between the abstract concepts, their geometrical interpretation, and the computational aspects of linear algebra.
% Mathematical reasoning is useful for building models of the real world.
% Linear algebra models vectors and vector quantities
% LA has lots of applications
Linear algebra is a powerful set of tools for modelling vector quantities and vector transformations.
Learning linear algebra will open many doors for you. You need linear algebra to understand machine learning, computer graphics, chemistry, economics, quantum mechanics, signal processing, etc. Vectors and matrices are used all over the place! If high-school math is modelling superpowers, then linear algebra is the vector-upgrade that teaches you how to model multivariable quantities and gives you the intuition for thinking about them.
If you understand the concepts presented in this book you’ll be able to understand the math in \emph{a lot} more of the science articles on Wikipedia.
% The book has some unique features that distinguish it form other linear algebra books.
This book differs from regular textbooks by the conversational tone it is written in and its focus on transferring the intuition behind the concepts and procedures. Each concept is illustrated through concrete examples and in connection with applications. The computer algebra system \href{http://live.sympy.org}{\texttt{sympy}} is used to illustrate tedious computational tasks.
%It’s important to know how to solve problems by hand, but it’s nice to check one’s answers using the computer. Other applications of \href{http://live.sympy.org}{\texttt{sympy}} include cheating on homework problems.
%The first chapter of the book is a detailed review of topics from high school math which ensure that all readers start from a solid base of knowledge about number sets, functions, and techniques for solving equations.
In order to make learning linear algebra more accessible, the book begins with a review chapter on numbers, algebra, equations, functions, and other prerequisite concepts from high school math.
Anyone should be able to pick up the material regardless of their mathematical background.
% Rather than taking a strictly theoretical or a computational approach to linear algebra the book mixes both aspects of the subject. Each section describes the \emph{why?} and the \emph{how?}, including computational tricks useful for pen-and-paper exams.
{\bf The author},
has 14 years of tutoring experience,
a B.Eng. in electrical engineering, a M.Sc. in physics, and a Ph.D. in computer science. The informal and concise style of writing is inspired by the author’s tutoring experience while the applications are sourced from his research experience.
\textbf{This is the deal.}
Give me 330 pages of your attention, and I’ll teach you everything you need to know about vectors, matrices, linear transformations, vector spaces, and applications of these concepts. The book in your hands is the only book you’ll need for your first-year linear algebra course.
\noindent
{\bf Contents:} \
\hspace{2mm} - {\sc high school math review} \
\hspace{2mm} - {\sc vectors} \
\hspace{2mm} - {\sc matrices} \
\hspace{2mm} - {\sc linear transformations} \
\hspace{2mm} - {\sc vector spaces} \
%\hspace{2mm} - {\sc inner product spaces} \
\hspace{2mm} - {\sc eigenvalues & eigenvectors} \
%\hspace{2mm} - {\sc matrix decompositions} \
\hspace{2mm} - {\sc sympy tutorial} \
\hspace{2mm} - {\sc introduction to quantum mechanics } \
See the table of contents and the concept maps for a more detailed view of material covered.