Linear Algebra Done Wrong
by Sergei Treil
Number of pages: 222
The title of the book sounds a bit mysterious. Why should anyone read this book if it presents the subject in a wrong way? What is particularly done "wrong" in the book? Before answering these questions, let me first describe the target audience of this text. This book appeared as lecture notes for the course "Honors Linear Algebra". It supposed to be a first linear algebra course for mathematically advanced students. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigorous mathematics that is presented in a "cookbook style" calculus type course. Besides being a first course in linear algebra it is also supposed to be a first course introducing a student to rigorous proof, formal definitions---in short, to the style of modern theoretical (abstract) mathematics. The target audience explains the very specific blend of elementary ideas and concrete examples, which are usually presented in introductory linear algebra texts with more abstract definitions and constructions typical for advanced books.
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by Keith Matthews - University of Queensland
This an introduction to linear algebra with solutions to all exercises. It covers linear equations, matrices, subspaces, determinants, complex numbers, eigenvalues and eigenvectors, identifying second degree equations, three–dimensional geometry.
by Arak Mathai, Hans J. Haubold - De Gruyter Open
This textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on theorems and proofs too much. It is also designed to be self-contained.
by Mohammed Kaabar
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 problems.
The book was designed specifically for students who had not previously been exposed to mathematics as mathematicians view it. That is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions.