Braver S. The Dark Art of Linear Algebra. An Intuitive Geometric Approach 2023

Textbook in PDF format

Most introductory linear algebra textbooks follow one of two paths into the subject: abstract and arcane (beginning with the vector space axioms), or computational and colorless (beginning with systems of linear equations). The Dark Art of Linear Algebra takes a little-known third path that winds through a fascinating geometric landscape. Guided along it, readers encounter linear algebra's central objects - linear maps and the matrices that represent them - before they descend into the valley of linear systems. By emphasizing geometry over algorithms and intuition building over axiomatics, The Dark Art helps beginners grasp linear algebra’s great power and rare beauty. And it does this concisely: Students can read this book from cover to cover in a single course. All the usual introductory topics are here, presented with unusual clarity and style by Seth Braver, winner of the Mathematical Association of America's Beckenbach Book Prize for his first book, Lobachevski Illuminated.
Acknowledgements.
Preface for Teachers.
Preface for Students.
Vectors.
Vocabulary.
Linear Transformations and Matrices.
Gaussian Elimination.
The Determinant.
Change of Basis.
Eigenstuff.
Projections and Least Squares.
Selected Answers
Index.
About the Author