How to self-study university-level linear algebra?
I recommend a beginner’s guide to linear algebra titled Linear Algebra For Dummies. It’s ideal for students outside the math major who are self-studying. The book is extremely accessible, requiring no strong mathematical background. Instead of overwhelming readers with a barrage of definitions and symbols right from the start, it first provides a comprehensive overview of linear algebra before diving into the simplest concepts. Every step is explained in detail—for example, “The goal of Gaussian elimination is to simplify the system”— “matrix multiplication is actually the composition of linear transformations.” It covers every detail, so even complete beginners can learn linear algebra through this book.
Linear algebra is a branch of mathematics that uses matrices to solve systems of linear equations. Its applications are wide-ranging, spanning many disciplines including sociology, game theory, computer programming, engineering, and business. This book is likely the simplest introductory text on linear algebra. Many concepts are explained using intuitive diagrams whenever possible. The author first tells readers that a vector equals direction plus magnitude, a linear transformation equals stretching/rotation/projection, and a determinant equals a volume scaling factor, before gradually introducing formulas and specific calculation processes. Unlike many textbooks that simply list formulas, this book explains every step of matrix operations (step by step), helping readers understand the reasoning behind each procedure. Some examples even highlight common pitfalls to help readers avoid making similar mistakes when solving problems.
The author, Mary Jane Sterling, is a university mathematics professor with many years of teaching experience, including teaching high school mathematics. Unlike professors who have spent their entire careers at the university level, she clearly understands the need for a transitional phase between high school and university mathematics. She breaks down university-level material into simple, easy-to-understand concepts, enabling students who struggled to grasp linear algebra in class to master the subject through this book. The author has also written two other algebra books, Algebra I For Dummies and Algebra II For Dummies, which are also highly beginner-friendly self-study guides.
